Varian's Microeconomics Core I, Chapter 16: Equilibrium, Chapter 32: Exchange

Translate the expression "r6 > p".

"The consumer is willing to give up "p" dollars per unit bought to get 6 units of a good. • r: reservation price

What does the function v(x) mean?

"V" stands for value, therefore "v" functions desribe the value of "x" amount of goods. • V(x) = ...

Suppose that a consumer always consumes 2 spoons of sugar with each cup of coffee. If the price of sugar is p1 per spoonful and the price of coffee is p2 per cup and the consumer has m dollars to spend on coffee and sugar, how much will they want to purchase?

# of cups purchased = m / (2p1 + p2) An equation that predicts that person's preferences is: 2 p1 z + p2 z = m • p: price • z: # of cups of coffee • m: income

Suppose that a consumer is consuming 10 units of a discrete good and the price increases from $5 per unit to $6. However, after the price change the consumer continues to consume 10 units of the discrete good. What is the loss in the consumer's surplus from this price change?

$10

Suppose that a budget equation is given by PIXI + P2X2 = m. The government decides to impose a lump-sum tax of u, a quantity tax on good 1 of t, and a quantity subsidy on good 2 of s. What is the formula for the new budget line?

(p1 + t) x1 + (p2 - s) x2 = m - u

What is a simplified form to express the following conditions if a consumer believes in both of them? • (x1, x2) ≥ (y1, y2) and • (x1, x2) ≠ (y1, y2)

(x1, x2) > (y1, y2) • What bullet point #1 means in practicality is that a consumer weakly prefers consumption bundle (x) over consumption bundle (y). • Bullet point #2 shows that the consumer isn't indifferent towards the two product bundles. This means in terms of microeconomics that the consumer strictly prefers (x) over (y).

A bundle (x1, x2) is preferred to a bundle (y1, y2) if and only if the utility of (x1, x2) is larger than the utility of (y1, y2). How do you state this in a short-hand microeconomic notation?

(x1,x2) > (y1,y2) if and only if u(x1,x2) > u(y1,y2)

Suppose that there were 25 people who had a reservation price of $500, and the 26th person had a reservation price of $200. 1) What would the equilibrium price be if there were 24 apartments to rent? 2) What if there were 26 apartments to rent? 3) What if there were 25 apartments to rent?

1) $500. 2) $200. 3) Any price between $200 and $500.

Suppose that the demand curve is given by D(p) = 10 − p What is the gross benefit from consuming 6 units of the good?

1) Find the area under the curve until q = 6. • Add the area of a rectangle and triangle 2) Rectangle: 6 times 4 = 24 Triangle: 6 times 6 times (0.5) = 18 3) Add the components to find total area: 42 • Gross Benefit: 42 BONUS PROBLEM: If the price changes from 4 to 6, what is the change in consumer's surplus? • When the price is 4, the consumer's surplus is given by the area of a triangle with a base of 6 and a height of 6; i.e., the consumer's surplus is 18. When the price is 6, the triangle has a base of 4 and a height of 4, giving an area of 8. Thus the price change has reduced consumer's surplus by $10.

Using an Edgeworth box, how is the Pareto Efficient Allocation found?

1) Find the contract curve by connecting all the points that lie on the tangent of each traders' most beneficial indifference curve.

Suppose that the demand curve for a good is given by D(p) = 100/p. What price will maximize revenue?

1) Total Revenue = (price) (quantity) 2) TR = (100/p) p = 100p + 1 3) d/dx 100p + 1 = 100 Since 100 is a constant, revenue is pD(p) = 100 which is a constant, all prices maximize revenue.

If D(p) = 12 − 2p, what price will maximize revenue?

1) Total Revenue = (price) (quantity) 2) TR = (12 - 2p) p = 12p - 2p^2 3) d/dx 12p - 2p^2 = 12 - 4p • p: 3 • ANS: $3

If a consumer has a utility function u(x, y) = x^1 y^4, what fraction of her income will she spend on good y? • x: good 1 • y: composite good 2

80% of their income. Because this is a Cobb-Douglas utility function, so she will spend 4 / (1 + 4) = 4/5 = 80% of her income on good 2.

subsidy

A government payment to the people that is meant to support a business or market

rationing

A limited portion or allowance of food or goods to be purchased for a consumer; limitation of use

budget line

A line that shows the different combinations of two products a consumer can purchase with a specific money income, given the products' prices

Income elasticity of demand (YED)

A measure of the responsiveness of demand to changes in income; the percent change in quantity divided by the percent change in income

Monotonic Transformation Principle

A monotonic transformation of a utility function is a utility function that represents the same preferences as the original utility function.

Describe the characteristics of a theoretically perfect rate of inflation?

A rate in which all prices and all incomes rise at the same rate. This means that there is no change anybody's budget set, and thus cannot change anybody's optimal choice.

What does it mean when something is Pareto efficient?

A situation is Pareto efficient if there is no way to make some group of people better off without making some other group worse off. • The Pareto efficient amount of output to supply in a single market is that amount where the demand and supply curves cross, since this is the only point where the amount that demanders are willing to pay for an extra unit of output equals the price at which suppliers are willing to supply an extra unit of output.

short-run supply curve

A supply curve during a short timeframe; shows the quantity of a product a firm in a purely competitive industry will offer to sell depending on various prices in the short run; the portion of the firm's short-run marginal cost curve that lies above its average-variable-cost curve

economy

A system for producing and distributing goods, as well as services to fulfill people's wants

Direct Demand Function

A table, a graph or an equation that shows how quantity demanded is related to product price, holding constant the five other variables that influence demand: Qd = f(p).

income tax

A tax only based on people's earnings • contrast this with a quantity tax, which is based only on the quantity of goods a consumer purchases.

What do you suppose the effect of a tax on apartments for landlords would be on the number of apartments that would be built in the long run?

A tax would undoubtedly reduce the number of apartments supplied in the long run.

A) How would an auctioner change the price of their goods if they were in excess demand? B) If they were in excess supply?

A) Price would be raised B) Price would be lowered

A good can be produced in a competitive industry at a cost of $10 per unit. There are 100 consumers are each willing to pay $12 each to consume a single unit of the good (additional units have no value to them.) A) What is the equilibrium price and quantity sold? B) The government imposes a tax of $1 on the good. What is the deadweight loss of this tax?

A) The equilibrium price is $10 and the quantity sold is 100 units. B) If the tax is imposed, the price rises to $11, but 100 units of the good will still be sold, so there is no deadweight loss.

A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. A) Is this preference relation transitive? B) Is it complete?

A) Yes, it is transitive. B) But it's not complete. • Because it's possible that a player could be bigger but slower than another, and vice versa.

What is an example of a consumption externatily?

Agent A cares about agent B's consumption of cigars Therefore, after each person has purchased the best bundle he or she can afford, there may still be ways to make both of them better off—such as A paying B to smoke fewer cigars.

Pareto inefficient

An allocation isn't fully optimized for the mutual benefit of both the buyer and the seller; an allocation that has the potential to be optimized with a Pareto improvement • EX: a monopoly greatly benefits the seller, but hurts the buyers, therefore it has room for Pareto improvements • EX: Rent control can be good for certain buyers but it hurts the sellers

Budget Line Equation (XY Notation)

An equation that conveys how how much an entity can spend based on their income and the prices of desired goods

Budget Line Equation (Varian's Notation)

An equation that conveys how how much an entity can spend based on their income and the prices of desired goods • m: total household income • x2: composite good • x1: a specific good

condominium

An individually owned housing unit in a building with several such units

What are some pairs of goods for which your preferences might be concave?

Any combination of things that you like separately but not together: • Peanut Butter and Pizza • Sushi and Ice cream • Sex and children • Alcohol and driving

What are some qualitative effects of a tax?

As the tax on a good increases: 1) The quanitity of the good sold decreases 2) The price paid by demanders increases 3) The price received by suppliers decreases

optimal level of demand for good 1

At the optimal level of demand for good 1 p1 = p2 | MRS |

When a tax is levied on a vendor's goods, which consequence is generally more detrimental to the vendor? A) The increase in the price paid by the demanders and decrease the price received by the suppliers. B) The output the vendor sells will be reduced.

B) It's true that taxing a good will typically increase the price paid by the demanders and decrease the price received by the suppliers. This certainly represents a cost to the demanders and suppliers. But from the economist's viewpoint the real cost of the tax is that the output has been reduced. The lost output is the social cost of the tax.

Why is it that not all preferences can be represented by utility functions?

Because ranking the order of bundles isn't possible when the consumer's preferences are intransitive preferences (aren't ordinal in nature) • EX: A consumer favors bundles in the following pattern: A > B > C > A John likes Snickers more than Reece's, and Recee's more than Milky Ways. But he also likes Milky Ways more than Snickers.

Why is it that taking a monotonic transformation of a utility function doesn't change the marginal rate of substitution?

Because the MRS is measured along an indifference curve, and utility remains constant along an indifference curve.

What is the equation that finds the interest rate of loans when taxes are included?

D( (1 − t) r' ) = S( (1 − t)r' ) • r' = r" / (1 - t)

Will every consumption bundle that's a part of the indifference curve have the same utility?

Each consumption bundle that lies on the indifference curve must have the same utility to that consumer. Since every bundle on an indifference curve must have the same utility, a utility function is a way of assigning numbers to the different indifference curves in a way that higher indifference curves get assigned larger numbers.

Economics proceeds by making ______ of social phenomena, which are simplified representations of reality.

Economics proceeds by making models of social phenomena, which are simplified representations of reality.

Cobb-Douglas Preferences

FUNCTION u(x1,x 2) = (x1^c) (x2^d) • c & d: positive #s that describe the preferences of consumers • c+d = 1 • EX: = √(x1x2)

True or false? If the demand function is x1 = −p1, then the inverse demand function is x = −1/p1.

False. The inverse demand function isn't defined as being the reciprocal fo the demand function. • Rather, you find the inverse by solving for price p as a function of demand.

How can you find using an Edgeworth Box what trades would make both traders benefit?

Find the region that shows where both traders are better off. 1) The Edgeworth box shows that the region that a trader will be better off is any region above their original endowment (W) curve. 2) Since the Edgeworth box shows two people's indifference curves, find the region that is above both trader's original endowments. • Remember that all of one of the trader's indifference curves are "up-side-down". 3) In the attached diagram, this area is denoted by the shaded region (M).

For what kind of preferences will the consumer be just as well-off facing a quantity tax as an income tax?

For kinked preferences, such as perfect complements, where the change in price doesn't induce any change in demand.

Income tax versus a quantity tax

Here we consider a quantity tax that raises revenue R and an income tax that raises the same revenue. The consumer will be better off under the income tax, since he can choose a point on a higher indifference curve.

collective action

How groups form and organize to pursue their goals or objectives • encourages participation and cooperation.

If all consumers are facing the same prices, then all consumers will have to have the ____ marginal rate of substitution between each of the two goods.

If all consumers are facing the same prices, then all consumers will have to have the same marginal rate of substitution between each of the two goods.

What can be determined about consumers' marginal rates of substitution when the prices of goods are universal (the same for each consumer)?

If everyone faces the same prices for the two goods, then everyone will have the same marginal rate of substitution, and will thus be willing to trade off the two goods in the same way.

What factors can determine if an aggregate excess demand functinon is continous?

If one or both of these conditions is true: • Each individual's demand function be continuous—that small changes in prices will lead to only small changes in demand (each consumer must have convex preferences) the aggregate demand function will be continuous. • Even if consumers themselves have discontinuous demand behavior, as long as all consumers are small relative to the size of the market, the aggregate demand function will be continuous.

How can studying a consumer's consumption choices be helpful in predicting future choices and estimating the the utility of new economic policies to consumers?

If several of a consumer's consumption choices are observed it may be possible to estimate a utility function that would generate that sort of choice behavior. Such a utility function can be used to predict future choices and to estimate the utility to consumers of new economic policies.

Should price be increased to generate more revenue if the demand for the goods is elastic? What about inelastic?

If the demand for a good is inelastic, increasing prices should result in more revenue. If it's elastic, price increases will hurt revenue.

complement

If the demand for good 1 goes down when the price of good 2 goes up, then good 1 is a complement to good 2. • Δx1/Δp2 is negative for perfect complements • EX: Sugar and coffee. If John must have a sugar to a coffee, then if coffee becomes more expensive, he will drink less coffee. And if he drinks less coffee, he will consume less sugar.

substitute

If the demand for good 1 goes up when the price of good 2 goes up, then we say that good 1 is a substitute for good 2. • Δx1/Δp2 is positive (or zero) for perfect substitutes • EX: Red and blue pencils. If Mary doesn't care what color pencili she uses, and blue pencils are more expensive than red pencils, she will buy red pencils instead.

Optimal choice with perfect complements

If the goods are perfect complements, the quantities demanded will always lie on the diagonal since the optimal choice occurs where x1 equals x2. m / (p1 + p2) = optimal choice • m: income • p: price

Optimal Choice with perfect substitutes

If the goods are perfect substitutes, the optimal choice will usually be on the boundary. • EX: 1 nickle < 1 dime Therefore, it would be better to have 5 dimes rather than 5 nickles.

If the inverse demand curve is a linear function p(q) = a − bq, then what expression gives the marginal revenue? • a: constant • q: quantity demanded • p: price • b:

If the inverse demand curve is a linear function p(q) = a − bq then the marginal revenue is given by MR = a − 2bq.

In general, the __________ variation and the __________ variation in income are used to measure the monetary impact of a price change.

In general, the compensating variation and the equivalent variation in income can be used to measure the monetary impact of a price change.

composite good

In the Budget Constraint Equation, An abstract variable that stands for a good or collection of several goods; usually everything else that the consumer might want to consume other than good x1. • m: total household income • x2: composite good • x1: a specific good

In the case of a perfectly elastic supply, how much of its tax gets passed along to the consumer?

In the case of a perfectly elastic supply curve the tax gets completely passed along to the consumers. • horizontal supply curve

In the case of a perfectly inelastic supply, how much of the tax gets passed along to the consumer?

In the case of a perfectly inelastic supply none of the tax gets passed along to the consumer. • vertical supply curve

Is an elasticity of −3 greater or less than an elasticity of −2?

In the context of elasticity, the absolue value of the number represents how elastic it is. The greater the magnitude of the absolute value, the greater the elasticity. • Economists tend to imply the negative sign rather than write it(EX: "2" means -2). So, -3 has greater elasticity than -2.

nonconvex preferences

In the context of monotonicity, the event of when points between two extreme consumption bundles have the possibility of being preferred or not preferred • see diagram • NOTE: A point represents a consumption bundle. The shaded region represents when the consumer prefers a bundle. So, when a point lies within the shaded region, it means that the consumption bundle is preferred.

Concave Preferences

In the context pf monotonicity, two extremes consumption bundles are preferred to the average of both goods • see diagram • NOTE: A point represents a consumption bundle. The shaded region represents when the consumer prefers a bundle. So, when a point lies within the shaded region, it means that the consumption bundle is preferred. • EX: John likes olives, and ice cream. But he doesn't like them together.

venture capitalists

Individuals or companies that invest in new businesses in exchange for partial ownership of those businesses

If goods 1 and 2 are complements, will increasing the price of good 2 will shift the aggregate demand curve for good 1 inward or outward?

Inward.

How does the amount of a consumer's income affect their reservation prices if they have quasilinear preferences?

It doesn't. In the special case of quasilinear utility the reservation prices are independent of the amount of money the consumer has to spend on other goods.

What does monotonicity imply about the shape of indifference curves?

It implies that they have a negative slope.

As the supply curve becomes steeper, does more or less of the cost of a tax on a good sold get passed along to the consumer?

Less-- the cost of the tax increasingly costs the vendor rather than the consumer as the supply curve becomes less elastic.

How is it that luxary goods are able to have income elasticities greater than one and yet normal elasticities are still able to be about 1?

Luxury goods that have an income elasticity greater than 1 must be counterbalanced by goods that have an income elasticity less than 1, so that "on average" income elasticities are about 1.

What is a formula that relates marginal revenue and elasticity?

MR = p[1 + 1/e] = p[1 − 1/ |e| ] • e: price elasticity of demand • IeI: absolute value of e • p: price of good • MR: marginal revenue

What does the term marginal mean in terms of mathematics?

Marginal means that a derivative is being found. • Study Calculus if you don't know what that means.

Demand Function

Mathematical relationship where quantity demanded is a function of price • "D(p)"

Demand Function

Mathematical relationship where quantity demanded is a function of price and income Notation • x1 = (p1, p2, m) • x2 = (p1, p2, m) • x: quantity of goods demanded • m: income of the consumer • p: prices of goods

Can an indifference curve cross itself or other indifference curves?

No. • see diagram • Indifference curves can't possess a positive slop.

If the preferences are concave will the consumer ever consume both of the goods together?

No. Concave preferences can only give rise to optimal consumption bundles that involve zero consumption of one of the goods.

What is an example of a Giffen Good?

Once, Donald Trump faced competitors in the apartment industry that were losing money. His competitors lowered the prices of their apartments. Trump's advisors suggested that he lower his prices to maintain sales and competition. But Trump defied the suggestions by instead raising the prices of his apartments, without improving them or making any significant changes. Trump cited that he felt as though apartment clients of such a high class wanted to buy the best apartments possible. Therefore, increasing the prices as his competitors decreased them would increase demand, as the customers wanted what they precived to be the best apartments rathethan the most affordable. Trump gained significant market share after the price change, and his competitors went out of business.

Only _______ prices are determined in a general equilibrium system.

Only relative prices are determined in a general equilibrium system.

ordinary goods

Ordinarily, the demand for a good increases when its price decreases.

If goods 1 and 2 are substitutes, will increasing the price of good 2 will shift the aggregate demand curve for good 1 inward or outward?

Outward.

equilibrium equation when tax isn't imposed on suppliers

Pd(q) - t = Ps(q) • Pd: Total price of goods at a specified demand • q: specified quantity • t: tax levied • PS: Price of corresponding supply

equilibrium equation when tax is imposed on suppliers

Pd(q) = Ps(q) + t • Pd: Total price of goods at a specified demand • q: specified quantity • t: tax levied • PS: Price of corresponding supply

What determines if a machine is profitable?

Profitable machines are characterized their outputs as being more valuable than their inputs Worthless machines are characterized by their outputs as being less valuable than their inputs.

What will happen to revenue if there's an increase in supply but the demand is inelastic?

Revenue will decrease. • If demand is elastic, then an increase in quantity will result in an increase in revenue.

perfect substitutes Engel Curve

Since the demand for good 1 is x1 = m/p1 in this case, the Engel curve will be a straight line with a slope of p1, as depicted • the attached graphs represents the demand behavior of perfect substitutes

homothetic preferences

Tastes for which the marginal rate of substitution doesn't change as long as the ratio of goods x1 to goods x2 remains constant • EX: If a comsumer has homothetic preferences for (x1, x2) and (y1, y2), and prefers (x1, x2) to (y1, y2), then that means that this expression will be true for any positive value of t: (tx1, tx2) > (ty1, ty2) • the attached graphs show homothetic preferences for an income offer curve and Engel curve • These preferences are convienient but often not realistic.

What symbol do should be used to denote that a consumer strictly prefers one consumption bundle (x) over another consumption bundle (y)?

The "greater than" or "less than" symbol(s). (x1, x2) > (y1, y2)

What symbol do should be used to denote that a consumer is indifferent to either one consumption bundle (x) or another consumption bundle (y)?

The "~" symbol. (squiggly line) (x1, x2) ~ (y1, y2)

What symbol do should be used to denote that a consumer weakly prefers one consumption bundle (x) over another consumption bundle (y)?

The "≤" or "≥" symbols. (x1, x2) ≥ (y1, y2)

Are Cobb-Douglas preferences homothetic preferences? Why or why not?

The Cobb-Douglas utility function has the property that u (tx1, tx2) = (tx1)^a (tx2)^(1 − a) = t^a t^(1−a) x1^a x2^(1−a) = tx1^a x2^(1−a) = tu(x1,x 2). Thus if u(x1,x 2) >u (y1,y 2), we know that u(tx1, tx2) > u (ty1, ty2), so that Cobb-Douglas preferences are indeed homothetic.

What is in general the most important feature of a good that influences demand?

The consumer's demand function for a good will in general depend on the prices of all goods and income.

Suppose that the demand curve is vertical while the supply curve slopes upward. If a tax is imposed in this market who ends up paying it?

The consumer.

If two goods are perfect substitutes, what is the demand function for good 2?

The demand function for pefect substitutes depends on which good is more expensive. 1) x2 = 0 when p2 > p1 2) x2 = m/p2 when p2 < p1 3) anything between 0 and m/ p2 when p1 = p2 • p: price • x: a type of good EX: Nickles and Dimes. It's better to have 5 dimes and zero nickles than 5 nickles and 0 dimes. But it doesn't matter if you have 2 nickels or 1 dime.

Suppose that the city council decides that there should be a tax on apartments of $50 a year. Thus each landlord will have to pay $50 a year to the city for each apartment that he owns. How will the price of apartments change, if any?

The equilibrium price of the apartments shouldn't change. Because the supply curve remains constant; there is the same quantity of apartments and demand for apartments.

Marginal Willingness to Pay (MWTP)

The largest amount the person is willing to pay for an additional unit • measured by the slope of the indifference curve

Marginal Willingness to Pay (MWTP)

The largest amount the person is willing to pay for an additional unit of a good • The height of the demand curve at a given level of consumption measures the marginal willingness to pay for an additional unit of the good at that consumption level.

rationing constraints

The level of consumption of some good is fixed to be no larger than some amount.

How would the budget line be affected if the income the person made increased?

The line would shift up. • The prices of goods aren't affected • The slope isn't affected • The line would shift down if there was a decrease in profit

What is a cause of excess burden?

The lost value to the consumers and producers due to the reduction in the sales of a good. This reduction of sales is due to an increase in tax.

Composite-good convention

The lumping together of all goods that a person buys except for one specific good into a single portmanteau good • EX: Say Ashton buys a Snickers, Reece's, Milky Way, and Skittles. If Snickers is the chocolate bar being considered, then the Reece's, Milky Way, and Skittles can be thought of as one entity rather than many separate purchases.

Gross Consumer Surplus (gross benefit)

The maximum price a consumer is willing to pay for a good or bundle of goods; the total benefit a consumer receives for using a product • Calculate this by finding the area under the line up to q • q: the number of units a consumer will buy for their reservation price

Optimal choice with concave preferences

The optimal choice is the boundary point, Z, rather than the interior tangency point, X, because Z lies on a higher indifference curve. • EX: Olives and Ice cream. John likes olives, and he likes ice cream. But he doesn't like them together. This means his preferences are concave rather than convex. The optimal choice is a boundary point because he chooses to eat one or the other, not both.

Optimal Choice equation for Cobb-Douglas preferences

The optimal choices for Cobb-Douglas preferences are given by the equation. (p1x1 / m) = x1 ( c / (c + d) ) = x1 x2 = d / (c + d)

If the price of a good is increased by 1%, and the good has elastic demand, how will the quantity demanded be affected?

The quantity demanded decreases by more than 1%. • An elastic demand curve is one for which the quantity demanded is very responsive to price.

price ratio

The rate at which the market will exchange one product for a certain amount of another product

How would the budget line be affected if the price of good x1 was increased?

The slope becomes steeper. • The maximum amount of good x2 that the person would buy remains the same, since their income remains the same and the price of good x2 remains the same. • The slope becomes flatter when the price of x2 increases.

economics

The study of how people take initiative to satisfy their needs and wants; study of allocating limited resources with dynamic, unconstrained demand

The study of how the equilibrium price and quantity change when the underlying demand and supply curves change is another example of _________ statics.

The study of how the equilibrium price and quantity change when the underlying demand and supply curves change is another example of comparative statics.

What's an equation that expresses the supply of loan that a vendor will provide as a result of after-tax interest rates?

The supply of loans, which depends on the after-tax interest rate, is: S ( (1 − t) r ) = Supply of Loans

How is it that a vendor's revenue can increase even if the demand for their goods drops?

The vendor might have raised the price of their goods in such a way where demand decreased slightly but still generates more revenue. • Notice the relationship between price elasticity and revenue

What happens to the budget line if the price of good 2 increases, but the price of good 1 and income remain constant?

The vertical intercept decreases and the horizontal intercept stays the same. Thus the budget line becomes flatter.

If utility is quasilinear, are the compensating variation, the equivalent variation, and the change in consumer's surplus all equal?

They are all equal. • Even if utility is not quasilinear, the change in consumer's surplus may serve as a good approximation of the impact of the price change on a consumer's utility.

Are perfect substitutes are an example of homothetic preferences? Why or why not?

They are. The utility function for perfect substitutes is: u (x1, x2) = x1 + x2 Thus, if u (x1, x2) > u (y1, y2) then we have x1 + x2 > y1 + y2. It follows that tx1 + tx2 > ty1 + ty2 so that u (tx1, tx2) > u (ty1, ty2)

How can the Edgeworth box be used to study the bargains of many people, rather than just two people?

Think of the Edgeworth box as depicting the average demands in an economy with only two types of consumers, but with many consumers of each type.

If the market demand curve is D(p) = 100 − 0.5p, what is the inverse demand curve?

To find an inverse demand curve using the demand curve, solve for p : • ANSWER: P(q) = 200 − 2q

"In a two good model if one good is an inferior good the other good must be a luxury good." Is this statement true or false?

True. The weighted average of the income elasticities must be 1, so if one good has a negative income elasticity, the other good must have an elasticity greater than 1 to get the average to be 1.

Generally speaking, how elastic are perfect subsitutes?

Very elastic. • EX: Say blue and red pencils have the same price, and people don't care which kind they write with. If the price of red pencils increase by even just a little, the demand for red pencils will probably drop drastically as long as the price of blue pencils is cheaper.

What is the form of the inverse demand function for good 1 in the case of perfect complements?

We know that x1 = m/(p1 + p2). Solving for p1 as a function of the other variables, we have p1 = (m / x1) − p2.

How can tax be computed if the total price paid by a customer and the net value recived by the vendor are known?

When a good is taxed, there will always be two prices: the price paid by the demanders and the price received by the suppliers. The difference between the two represents the amount of the tax.

weighted average of the two bundles

When dealing with monotonicity, averages of two consumption bundles are preferred to extreme bundles • EX: A child wants as much candy as they can get. But realistically, they don't really want a warehouse full of candy.

Monopoly in the Edgeworth Box

When one of the traders (A) in an Edgeworth box acts as a monopoly rather than a fair trader, they will strive to recieve the best possible deal for A that trader B will accept, without concern of the best possible deal B could have; a pareto inefficient allocation in which only one of the traders benefits as much as possible • Trader A chooses the point on trader B's offer curve that gives A the highest utility. (As little compromise as possible to facilitate a deal.) • The indifference curves of the two traders will intersect but won't be tangent. • B's price offer curve will be tangent to A's indifference curve (instead of B's indifference curve being tangent to A's indifference curve) • See attached diagram

tangency condition

When the budget line is tangent to the highest indifference curve, that point describes the optimal choice.

In an Edgeworth Box, if an indifference curves of each of the two traders cross, what does that mean?

When the indifference curves of two seperate traders cross (rather than being tangent), the point of intersection represents a trade that can't be Pareto efficient (meaning a trade possible but inefficient trade could take place, where one trader is better off than the other). • Diagram: the red dot represents an inefficient trade.

What happens to the equilibrium price of a good when its corresponding supply curve and demand curve shifts to the left by the same amount?

When the supply of a good being sold is decreased, the equilibrium price is expected to increase. And as demand decreases, the price is expected to increase. • When a curve shifts to the left, it signified a decrease. Therefore, if the equilibrium price both increases and decreases by the same amount it remains the same.

If the marginal rate of substitution is different from the price ratio, does that mean the consumer is at their optimal choice?

Whenever the MRS is different from the price ratio, the consumer cannot be at his or her optimal choice.

Does Walras' Law hold true for all prices of goods?

Yes, Walras' Law must hold for all prices, since each agent must satisfy his or her budget constraint for all prices. • The value of how much one of the agents wants to buy of good 1 plus the value of how much she wants to buy of good 2 must equal zero. • Note: The amount that that agent wants to buy of one of the goods must be negative because they intends to sell some of one of the goods to buy more of the other.

Can one of two traders be made better off if they are at a Pareto efficient allocation?

Yes, but not without making someone else worse off.

Can the concept of Pareto efficiency be used to evaluate different ways of allocating resources?

Yes.

Is it possible for a competative equilibrium not not exist at all?

Yes.

Is the market equilibrium Pareto efficient?

Yes.

Does an increase of consumer income tend to lead towards an increase of demand in goods they like?

Yes. Therefore, as income (m) increases, the aggregate demand curve tends to shift outward

Does the Internal Revenue Service (IRS) sometimes allow borrowers to deduct their interest charges?

Yes. D ( (1 − t) r ) = Demand of Loans

If good 1 is a neutral good, what is its marginal rate of substitution for good 2?

Zero — if you take away some of good 1, the consumer needs zero units of good 2 to compensate them for their loss.

Suppose that the supply curve is vertical. What is the deadweight loss of a tax in this market?

Zero. The deadweight loss measures the value of lost output. Since the same amount is supplied before and after the tax, there is no deadweight loss. The suppliers are paying the entire amount of the tax, and everything they pay goes to the government. The amount that the suppliers would pay to avoid the tax is simply the tax revenue the government receives, so there is no excess burden of the tax.

consumption bundles

a collection of various goods or services that a consumer could consume • comprised of at least two types of goods • notation: (x2, x1) • EX: 5 bars of chocolate (written as x1) and 5 fruits (written as x2).

bad

a commodity that the consumer doesn't like • EX: Say John likes pepperoni on pizza but not pineapple. If John received a pizza with pineapple, how much pepperoni would the pizza have to have for John to remain indifferent to the pizza?

competitive equilibrium

a condition in which profit-maximizing producers and utility-maximizing consumers in competitive markets with freely determined prices arrive at an equilibrium price • the quantity supplied is equal to the quantity demanded • both buyers and sellers are satisfied that they're getting a fair deal

demanded bundle

a consumer's optimal choice of goods 1 and 2 at a specific set of prices and income

long-run supply curve

a diagram that shows the relationship in long run of how much supply will be offered based on various prices

continuous function

a function that can be graphed with a line or a smooth curve, because there are infinite points on the graph rather than discrete points

Giffen goods

a good for which an increase in the price raises the quantity demanded, and a decrease in price lessens demand • EX: Some people buy things for status and precieved premium quality.

numeraire good

a good for which the price is hypothetically set at $1 to model choice between goods, which depends on relative rather than absolute prices • numeraire: relative comparisons

neutral good

a good that the consumer doesn't particularly desire or find undesirable; a good for which demand does not change as income rises or falls • Marginal Rate of Substitution is infinite • EX: John neither likes or dislikes anchovies on his pizza. But he likes pepperoni.

Engel Curve

a graph of the demand for one of the goods (x1 or x2) as a function of income, with all prices being held constant

market supply curve

a graph of the quantity of a good supplied by many suppliers at different prices • conveys weighted averages of the prices from all the competive vendors

demand curve

a graph of the relationship between the price of a good and the quantity of goods demanded where quantity is a function of price • demand depends on price • P(q) • x1 = am / p1

supply curve

a graph of the relationship between the price of a good and the quantity the vendor supplies • measures the amount that will be supplied at each price • area under curve: the surplus enjoyed by the demanders of a good • area above curve: surplus enjoyed by the suppliers of a good (Producers surplus)

Demand Curve

a graph of the relationship of how much demand is generated because of a specific price • reservation prices determine how much of a good will be sold

price ceiling

a legal maximum on the price at which a good can be sold NOTATION • pc or pmax: price ceiling

competitive market

a market in which there are many buyers and many sellers so that each has a negligible impact on the market price

competative market

a market in which there are many buyers and many sellers so that each has a negligible impact on the market price • competition encourages lower prices to the buyer and innovation, while discouraging monopolies

competative market

a market in which there are many buyers and many sellers so that each has a negligible impact on the market price; market in which the demand for each good varies continuously as prices vary, so that there will always be some set of prices where demand equals supply in every market

monopoly

a market in which there are many buyers but only one seller • illegal

price elasticity of demand (e)

a measure of how much the quantity demanded of a good responds to a change in the price of that good; computed as the percentage change in quantity demanded divided by the percentage change in price • ratio of price to quantity multiplied by the slope of the demand function • derivative of the demand function

indifference curve

a model of a curve that illustrates the satisfaction consumers feel towards consumption bundles based on the ratio of one type of good (x1) to another type of good (x2). • this model assumes the transitive axiom is true (which may not always be the case realistically) SEE DIAGRAM (horizontal axis represents # of x1 goods) (vertical axis represents # of x2 goods) KEY • anything point that lies above the line represents a preferred bundle • any point that lies below the curve represents an undesired bundle • any point that is a part of the line represents an indifferent bundle

Edgeworth box

a model that depicts the distribution of goods in a scenerio where there are exactly two goods being traded and two parties trading, assuming the allocations are feasible • conveys preferences of two individuals • studies general equilibrium • Video Explanation: https://youtu.be/7QFAQJBq1uk KEY • black curves: indifference curves of one of the traders (trader A) • blue curves: indifference curves of the other trader (trader B) • Top and bottom lines of box (x1b): quantity of good #1 • Left and right lines of box (x'a): quantity of good #2 • Voice memo attached to this card. • NOTE: An Edgeworth box is the indifference curves of two seperate individuals (A & B) plotted on top of each other. Turn the box 180° to see the curve of individual B.

portmanteau

a new word formed by joining two others and combining their meanings • EX: Say Ashton buys a Snickers, Reece's, Milky Way, and Skittles. If Snickers is the chocolate bar being considered, then the Reece's, Milky Way, and Skittles can be thought of as one entity rather than many separate purchases.

monotonic

a pattern of association in which the value of cases on one variable increases or decreases fairly regularly across the categories of another variable

effective price

a price that would induce consumers to demand a specified amount NOTATION • specific demand: qe

trapezoid

a quadrilateral with exactly one pair of parallel sides

tax concessions

a reductions in taxes in response to demand • EX: A company is granted and exemption from paying tax for a period of time.

model

a representation of an object, event, or market

convex set

a set in which every segment that connects points of the set lies entirely in the set • see diagram

externalities

a side effect of an action that affects a third party other than the buyer or seller

inelastic demand

a situation in which an increase or a decrease in price will not significantly affect demand for the product • occurs when the elasticity of a good is less than 1 in absolute value

elastic demand

a situation in which consumer demand is sensitive to changes in price • a good has an elasticity of demand greater than 1 in absolute value

market equilibrium (competitive equilibrium) (Walrasian equilibrium)

a situation in which the quantity of goods demanded in a market equals the quantity of goods supplied • a set of prices exists such that each consumer chooses their most preferred affordable bundle • In market equilibrium, assuming each agent is choosing the best bundle that they can afford, the marginal rate of substitution between the two goods must be equal to the ratio of the prices

Pareto efficient

a situation is efficient if no change is possible that will help the buyer(s) or seller(s) without harming the other

axiom

a statement or proposition that is regarded as being established, accepted, or self-evidently true

high frequency trading

a subset of algorithmic trading that relies on computer programs to make very rapid trading decisions • instantaneous stock market trading

ad valorem subsidy

a subsidy based on the price of the good being subsidized

quantity subsidy

a subsidy in which the government gives an amount to the consumer that depends on theamount of the goods purchased

inverse supply curve

a supply curve written in the form of price as a function of quantity supplied; measures what price goods will be based on how much supply is availible • PS(q): inverse supply function • PD(q): inverse demand function • Equilibrium: PS(q) = PD(q)

value tax (ad valorem tax)

a tax based on the assessed value of an item • value subject to change EQUATION: PD = (1 + T) PS • PD: price the demander pays or receives • PS: price the supplier recieves or receives • T: tax rate • EX: real estate, personal property • ad valorem: "according to value"

quantity tax

a tax in which the consumer has to pay a certain amount to the government for each unit of the good they purchase EQUATION: PD = PS + t • tax • PD: price the demander pays or receives • PS: price the supplier receives or pays

value tax (ad valorem tax)

a tax in which the value is variable and depends on the price of the good being purchased rather than the quantity of goods purchased

distortionary tax

a tax that affects the economic behavior of individuals and corporations; taxing of labor that people decide to sell to the market • If the sale of labor is taxed, the labor supply decision of consumers will be distorted in that they will likely supply less labor than they would have supplied in the absence of a tax. Taxing the potential value of labor—the endowment of labor—is not distortionary.

lump sum subsidy

a tax that is a fixed amount for every person, regardless of their spending behavior

lump-sum tax

a tax that is a fixed amount for every person, regardless of their spending behavior

lump-sum tax

a tax that is the same amount for every person, regardless of earnings or any actions that the person might take

elasticity

a unitless measure of the responsiveness of quantity demanded or quantity supplied to a change in one of its determinants

exogenous variable

a variable that is assumed not to depend on the state of the economy—that is, it does not change when the economy changes • inelastic • models aren't focused on this variable • EX: prices of houses when someone is considering to buy only apartments

endogenous variable

a variable that is determined and significant within a model • EX: prices of apartments for someone considering to purchase apartments

utility

ability or capacity of a consumption bundle to be useful and give satisfaction to someone; description of consumer preferences

complete

all conditions are satisfied

weakly preferred set

all of the consumption bundles that are weakly preferred to a base consumption bundle

Pareto Efficient Allocation

allocation of goods in which no one can be made better off unless someone else is made worse off; the best possible trade that can transpire where both traders benefit as much as possible without comprimising the other trader • EDGEWORTH box: The pareto efficient allocation is represented by a point that lies on the tangent of each traders' most beneficial indifference curve, without hurting the other trader.

If two traders have convex preferences, then there will ______ be a set of prices such that each Pareto efficient allocation is also an equilibrium for some set of prices.

always

general equilibrium allocation

an allocation in which each agent chooses a most preferred bundle of goods from the set of goods that they can afford

circuit breaker

an emergency-use regulatory measure to temporarily halt trading on an exchange • designed to prevent stock market crashes • triggered based on S&P 500

interior optimum

an optimal basket at which a consumer will be purchasing positive amounts of all commodities

kinky tastes

an optimal consumption bundle in which the indifference curve doesn't have a tangent

boundary optimum

an optimal consumption choice that involves consuming zero units of one type of good • The indifference curve is not tangent to the budget line

Pareto improvement

any free market exchange of goods in which both the buyer and the seller benefit

perfect complements

are goods that are always consumed together in fixed proportions • EX: Water molecules are always composed of 2 hydrogen atoms and 1 oxygen atom. • Marginal Rate of Substitution can only be either is either zero or infinity • right-angle indifference curves

Reflexive axiom

assumption that any bundle is at least as good as itself (XI,X2) ≥ (XI,X2)

complete axiom

assumption that any two bundles can be compared

diminishing rate of substitution

assumption that as a consumer gains more of one good, they are more willing you to give some of it up in exchange for another good

transitive axiom

assumption that if the consumer thinks that consumption bundle X is at least as good as Y and that Y is at least as good as Z, then the consumer thinks that X is at least as good as Z. If (x2, x1) ≥ (y2, y1) and (y2, y1) ≥ (z2, z1) then (x2, x1) ≥ (z2, z1)

strict convexity

assumption that the weighted average of two indifferent bundles is strictly preferred to the two extreme bundles • The preferences for two goods that are perfect substitutes are strictly convex. • This might not always be the case in reality.

normative economics

branch of economics concerned with subjective notions about the way the economy should be conducted • morals • "How should people use money?" • determines value

onerous

burdensome

Axioms of Consumer Theory

certain assumptions about preference relations that are widely regarded to be true in the study of economics • Complete axiom • Reflexive axiom • Transition axiom

unit elastic demand

condition of the percentage change in quantity demanded equals the percentage change in price; the resulting price elasticity is -1 (and has an absolute value of 1).

perfectly inelastic supply

condition of the quantity of goods that a vendor sells is fixed, not being subject to change • price elasticity of supply value of zero • vertical supply curve • Equilibrium price of supply = price of supply - taxes (The entire amount of the tax is paid by the suppliers.)

Convex Preferences

condition of when the average of two extreme consumption bundles that the consumer is indifferent to are preferred to the bundles themselves • see diagram • NOTE: A point represents a consumption bundle. The shaded region represents when the consumer prefers a bundle. So, when a point lies within the shaded region, it means that the consumption bundle is preferred.

quasilinear utility

condition that the utility function is linear in good 2, but possibly non- linear in good 1 • "partly linear" utility

provisos

condition; stipulations as in a contract

Choice

consumers choose the most preferred bundle from their budget sets; the bundle in the consumer's budget set that lies on the highest indifference curve • Typically the optimal bundle will be characterized by the condition that the slope of the indifference curve (the MRS) will equal the slope of the budget line.

external costs

costs of a transaction that affect people other than the buyer or seller; the costs of a market activity paid by people who are not participants

concave

curving inward

convex

curving outward

Black Tuesday

date of the worst stock-market crash in American history and beginning of the Great Depression. • October 29, 1929

intransitive preferences

decisions based solely on preferences are irrational and cause intransitive cycles that delay decision making; preferences that aren't ordinal or predicatable

The income offer curve is to the Engel curve as the price offer curve is to the ______ ______.

demand curve

disequilibrium

describes any price or quantity not at equilibrium; market condition of quantity supplied not being equal to quantity demanded or vise vera

inframarginal

describing exchanges taking place "within" the margin, as opposed to "on" or "outside" the margin

satiation (bliss) point

during satiation, the ideal consumption bundle that the consumer wants and any deviation from it is perceived as negative • EX: John wants exactly one slice of cake and one scoop of ice cream

Quasilinear Preferences

each indifference curve is a vertically shifted version of a single indifference curve • EX: u(x1,x 2) = x1 + √x2

stock market crash (bubble burst)

event of stock prices dropping dramatically, an radical excess of sellers to buyers

pure exchange

exchanges that take place in which those who trade have a fixed quantity of goods and no production is involved

extreme consumption bundles

extreme in this context means two consumption bundles that different enough to be considered as significantly different. • EX: John doesn't care either way if he receives three or five skittles when he asks for some skittles but he would care if he received one-hundred or zero skittles.

after-tax interest rate

figure that reflects the amount of interest an loaner can keep for their loan after taxes have been deducted • the principle amount of loans aren't subject to taxation, but any revenue generated through interest rates are (1 - t) r = after-tax interest rate • t: rax • r: rate • This equation assumes that everyone is in the same tax bracket.

utility function

formula used to rank the utility of individual consumption bundle relative to other bundles • magnitude of the differences in utility of bundles isn't taken into account; doesn't measure the utility itself, just the relative order NOTATION • u: utility

inverse demand function

function where price of a good is a function of quantity demanded; measures what the market price for a good would have to be for a specified quanitiy of them to be demanded

normal goods

goods for which demand increases when the consumer's income increases and demand decreases when income decreases

inferior goods

goods for which demand tends to fall when the consumer's income rises • ramen noodles for a college student

luxary goods

goods in which demand increases by a greater proportion than consumer income

necessary goods

goods in which demand increases by a lesser proportion than consumer income • Q-Tips

continuous goods

goods that are measured in continuous amounts rather than discrete integers • EX: What exact distance has John driven? 3.4839... mi

discrete good

goods that are measured in discrete, integer quantities rather than continuous amounts • EX: How many cars does John own? 2.

Optimal choice with discrete goods

goods that are only available in integer amounts

discrete goods

goods that are only available in integer amounts

aggregate excess demand function

graph of aggregate excess demand • usually a continuous function • generally, small changes in prices should result in only small changes in aggregate demand

extensive margin

how many more or fewer people buy a product when its price changes • Rule of Thumb: the cheaper the good, the more customers are attracted

intensive margin

how much more or less of a good consumers buy when its price changes • Rule of Thumb: The cheaper something is, the more each customer tends to buy.

This card is just a YouTube link explaining Pareto Efficient Allocations and contract curves.

https://youtu.be/7QFAQJBq1uk

S&P 500 (Standard & Poor's 500)

index that shows the price changes of 500 different stocks

gross complements

inputs such that when the price of one changes, the demand for the other changes in the opposite direction because the output effect exceeds the substitution effect.

gross substitutes

inputs such that when the price of one changes, the demand for the other changes in the same direction because the substitution effect exceeds the output effect

invisible hand

jargon refering to the principle that the economy tends to correct itself when its markets aren't in equilibrium due to the process of vendors acting in the interest of self-directed gain in a way that yeilds social and economic benefits for all • "Whenever there is a excess demand, vendors will produce more, and when there is excess supply, they will produce less." • "If excess demand exists in one market in an economy, there must be another market that experiences a lack of demand" • Either all of the markets are in perfect equilibrium or some markets are in partial equilibrium such that they offset each (they "cancel out"; ie -1 + 1 = 0) • phrase coined by Adam Smith

rent control

legislation that limits rental rates in a city or state; a price ceiling placed on rent; the maximum price rent is allowed to be as well as the amount that the rent can be increased per year • weakens apartment sellers' potential profits

vertical intercept of budget line

m / P2 m: slope p: price of x2

horizontal intercept of budget line

m / p1 m: slope p: price of x1

marginal utility function

marginal

inverse demand function

mathematical function that describes events when the value of a price of a good is a function of quantity of goods demanded; function that measures the price at which a given quantity will be demanded • price depends on quantity demanded • Q(p) • p1 = am / x1

Inverse Supply Function

mathematical relationship where the price the vendor sells their goods for is a function of the quantity they supply • function that measures what the price would have to be to get the producer to supply x units of the good • Notation: ps(x) = price at x units

demand function

mathematical relationship where the quantity of goods demanded is a function of prices and income • x1 (p1, p2, m) • x2 (p1, p2, m) • m: income • p: price • x: a type of good

income offer curve (income expansion path)

model that illustrates various bundles of goods that are demanded at the different levels of consumer income • positive slope: both goods are normal goods • For each level of income, m, there will be some optimal choice for each of the goods.

price offer curve

model that represents the optimal purchases that a consumer can make depending on what the prices of the goods are DIAGRAM • Panel A contains a price offer curve, which depicts the optimal choices as the price of good 1 changes. • Panel B contains the associated demand curve, which depicts a plot of the optimal choice of good 1 as a function of its price.

discriminating monopoly

occurs when a monopolist is able to charge different prices for identical products • maximum profit for the seller • EX: a monopolist landlord could decide to auction their apartments off one by one to the highest bidders. This means that different people would end up paying different prices for identical apartments.

How do you find the absolute value of the marginal rate of substitution?

p1 / p2 = | MRS |

well-behaved preferences

pattern of preferences that are monotonic and convex • "more is better" • averages are preferred to extremes

endowment of labor

potential value of labor

revenue

price of a good multiplied by the quantity sold • R = pq

equilibrium principle

principle that states a market reaches equilibrium as prices of goods adjust until the number of people that demand those goods are equal to the amount of goods supplied • No unexploited opportunities for individuals but may not exploit all gains achievable through collective action

optimization principle

principle that states people try to choose the best choice of consumption that they can afford

net demand (excess demand) (e)

quantity of goods that a consumer wants to purchase • total bundle of goods the purchaser has or wants after trading minus their initial endowment • net demand = gross demand - initial endowment • Notation: e • e'A = x'A - w'A

gross demand

quantity of goods that one desires to consume • net demand = gross demand - initial endowment • Notation: e'A = x'A - w'A

What is the value of r6 in terms of value functions?

r6 = v(6) - v(5) • Reservation price (r): the maximum price a consumer is willing to pay for a product or service; the threshold price between a consumer deciding to purchase or purchasing a good PATTERN • r1 = v(1) - v(0) • r2 = v(2) - v(1) • r3 = v(3) - v(2) • ... • In the case of a discrete good and quasilinear utility, the utility associated with the consumption of n units of the discrete good is just the sum of the first n reservation prices. • This sum is the gross benefit of consuming the good. If the amount spent is subtracted from the purchase of the good, then it's consumer's surplus.

ordinal utility

ranking of the utility of two or more consumption bundles

qualitative

relating to, measuring, or measured by the quality of something rather than its quantity

tax reforms

rewriting the taxes to change the rates and who pays them

change in revenue

roughly calculated as being equal to the quantity of a good times the change in price plus the original price times the change in quantity ΔR = qΔp + pΔq divide this expression by Δp to find the rate of change of revenue per change in price: ΔR / Δp = q + p (Δq / Δp)

marginal utility

satisfaction or usefulness obtained from acquiring one unit of a product

satiation

situation in which a consumer is the most satisfied with one particular bundle, and any deviation from that bundle is perceived as negative

marginal changes

small incremental adjustments

Second Theorem of Welfare Economics

states that any efficient allocation can be attained as a competitive equilibrium, since the market mechanisms lead to redistribution • if all agents of a trade have convex preferences, then there will always be a set of prices such that each Pareto efficient allocation is also an equilibrium for some set of prices • implies that any desired Pareto optimal outcome can be supported • Pareto efficiency can be achieved with any redistribution of initial wealth but attempts to correct the distribution may introduce distortions, and so full optimality may not be attainable with redistribution • implies that prices should be adjusted to reflect scarcity

Walras' Law

states that in a general equilibrium model, one of the market clearing constraints is redundant and will hold if all other constraints hold; this means the value of aggregate excess demand is zero for all prices • in a world with n markets, if n-1 markets are in equilibrium, the the nth market must be as well • If an excess demand of one trader in the Edgeworth box is eqaul to zero, then the other trader's must be as well. • EX: If z' (p1 , p2 ) = 0 then z" (p1, p2 ) = 0 must be true as well • https://youtu.be/OPRu6DZKOfc

partial equilibrium

study of an equilibrium in one market, ignoring the rest of the economy • Since in general the prices of other goods affects demand and supply for a particular good, partial equilibrium can be misleading and inadequate.

initial endowment allocation (w)

the allocation of goods that traders begin a trade with, before any trading has taken place • Not all of these goods necissarily have to be traded. Notation: (w'a, w"a) • A (or B): a trader • w': initial allocation of good 1 • w": initial allocation of good 2

final allocation

the allocation of goods that traders finish with, after all trading has taken place • Some of these goods could be the same as their intitial allocation bundle

Aggregate Demand (AD)

the amount of total spending on domestic goods and services in an economy

positive economics

the branch of economic analysis that describes the how the economy works • objective rather than subjective • "Why do people use money?"

Marginal Utility (MU)

the change in total utility a person receives from consuming one additional unit of a good or service

consumption bundle

the collection of all the goods and services that an individual chooses to consume

comparative statistics

the comparison of economic outcomes before and after some economic variable is changed; the study of how the equilibrium price and quantity change when the underlying conditions change • EX: changes in prices of a good to see how it affects demand

consumption externality

the condition of one party in a trade being concerned with what the other trader(s) consume because of the trade, rather than only being concerned with what they themselves stand to gain; an externality that affects the consumption side of a market, which may be either positive or negative • When consumption externalities are present, a competitive equilibrium need not be Pareto efficient.

Monotonicity of preferences

the condition that a consumer perceives having more goods as being better

general equilibrium

the condition that exists when all markets in an economy are in simultaneous equilibrium; demand and supply conditions interact in several markets to determine the prices of many goods; study of how the economy can adjust to have demand equal supply in all markets at the same time

excess demand (shortage)

the condition that exists when quantity demanded exceeds quantity supplied at the current price

quantity tax

the consumer has to pay a certain fixed amount to the government for every unit of the good purchased

private costs

the costs of an economic activity directly borne by the immediate producer or consumer (excluding externalities)

market demand curve

the demand curve that shows the quantities demanded by everyone who is interested in purchasing the product • sum of individual demand curves

consumer surplus (net consumer surplus)

the difference between the amount a buyer is willing to pay for a good and the amount the buyer actually pays • CS = v(n) - pn • n: # of goods, p: price, CS: Consumer Surplus • EX: John is willing to pay up to $30,000 for a new car. He buys a new car for $10,000. Therefore the consumer surplus is $20,000.

product surplus

the difference between the amount a seller is paid for a good and the seller's true cost of providing it • Say it costs Nike $25 to manufature silver Converses, and they sell those shoes to consumers for $70. The product surplus is $45.

Net Producer's Surplus

the difference between the minimum amount a vendor would be willing to sell some units for and the amount she actually sells those units for

Producers Surplus (PS)

the difference between the price sellers receive for a good and the minimum or lowest price for which they would have sold the good • area above supply curve

Great Depression

the economic crisis beginning with the stock market crash in 1929 and continuing through the 1930s

Marginal Revenue (MR)

the extra revenue associated with selling an extra unit of output; the change in total revenue with a one-unit change in output

deadweight loss

the fall in total surplus that results from a market distortion, such as a tax

externality

the impact of one person's actions on the well-being of a bystander; an economic side effect of a good or service that generates benefits or costs to someone other than the person deciding how much to produce or consume

original endowment (w)

the initial allocation of good between traders before any trading has taken place

budget constraint

the limited amount of income available to consumers to spend on goods and services

equivalent variation (EV)

the maximum amount of money a consumer would be willing to lose in order to avoid dealing with a price increase

reservation price

the maximum price a consumer is willing to pay for a product or service based on the total perceived consumer benefits

reservation price

the maximum price a consumer is willing to pay for a product or service; the threshold price between a consumer deciding to purchase or purchasing a good • r: reservation price • p: price • x: quanitiy of good x u (0, m) = u(1, m − r1) u (1, m − r2) = u(2, m − 2r2) The left-hand side of this equation is the utility from consuming one unit of the good at a price of r2. The right-hand side is the utility from consuming two units of the good, each of which sells for r2.

compensating variation (CV)

the minimum amount of money a consumer would have to receive in the event of the price of a good increasing in order to completely offset completely the precieved harm a consumer feels from the price increase

Opprotunity Cost

the most desirable alternative given up as the result of a decision

expenditure share (market share)

the percentage of the total expenditure for an item that can be attributed to a particular subgroup

equilibrium price

the price of a good or service that causes the quantities of the good supplied to equal the number of people demanding the quantity; the price that maximizes total sales revenue

numeraire price

the price relative to which we are measuring the other price and income • "How many books can I afford if I have $(X) but I spend $(Y) on movies?"

numeraire price

the price relative to which we are measuring the other price and income • numeraire: relative comparisons

equilibrium price

the price that balances quantity of goods a vendor supplies and quantity demanded • D(p) = S(p)

optimal choice

the purchase a consumer can afford that makes that maximizes utility (satisfaction) • generally, the indifference curve is tangent to the budget line

marginal rate of substitution

the rate at which a consumer is willing to trade one type of good for another; a model that shows the change in slope of the indifference curve CALCULUS The marginal rate is the derivative of the indifference curve • EX: John likes Skittles more than M&Ms. He will trade 1 Skittle for 2 M&Ms (1:2 ratio). • rate: Δx2 / Δx1 • always a negative value

Marginal Rate of Substitution (MRS)

the rate at which a consumer would be willing to trade off one good for another

slope (m) of Budget Line Equation

the rate at which the market is willing to "substitute" good x1 for good x2 EQUATION m = p1x1 + p2x2 slope can also be viewed as -p1 / p2 • p1: price of good x1 • p2: price of good x2 • Economists sometimes say that the slope of the budget line measures the opportunity cost of consuming good x1.

deadweight loss of a tax (excess burden of a tax)

the reduction in economic welfare of taxpayers that exceeds the revenue raised by the government; a figure that measures the value of output that is not sold due to the presence of the tax • Calculated as the net loss in consumers' surplus plus producers' surplus that arises from imposing the tax

Deadweight Loss (DWL)

the reduction in total surplus that occurs as a result of a market inefficiency, where no party involved gains anything useful as a result of the inefficiency

level set

the set of all (x1, x2) such that u(x1, x2) equals a constant

budget set

the set of all possible bundles of goods and services that can be purchased with a consumer's income

Contract curve (pareto set)

the set of points representing final allocations of two goods between two people that could occur as a result of mutually beneficial trading between those people; a model that conveys Pareto Efficient allocations that could occur as a result of ideal trading • When the slopes are the tangent for the indifference curves of both parties, the point that lies on the tangent represents a mutually beneficial trade • typically, the contract curve will stretch from trader A's origin to B's origin

welfare economics

the study of how the allocation of resources affects economic wellness

aggregate excess demand (z)

the sum of the excess demands of each trader • Notation: z' (p1, p2) • z' (p1, p2) = e'A (p1, p2) + e'B (p1 ,p2) • Equilibrium is defined when the aggregate excess demand is equal to zero: z (p1, p2) = 0 • Walrus' Law states that if an excess demand of one trader in the Edgeworth box is eqaul to zero, then the other trader's must be as well. • EX: If z' (p1 , p2 ) = 0 then z" (p1, p2 ) = 0 must be true as well

social cost

the total cost of producing a good or service, including both the private cost and any external cost

market demand

the total demand by all the consumers of a given good or service NOTATION • i: an individual of a sample/population

monotonic transformation

the transforming of one set of numbers into another set of numbers in a way that maintains the original order of the numbers • EX: 1, 2, 3 If each number is multiplied by 2, the order remains the same (2, 4, 6). • Thus, given any one utility function, any monotonic transformation of it will represent the same preferences.

First Theorem of Welfare Economics (invisible hand theorem)

theory that a competitive market will naturally gravitate towards Pareto efficiency • because a competitive market will exhaust all of the gains from trading eventually • an equilibrium allocation achieved by a set of competitive markets

cardinal utility

theory that the size of the utility difference between two bundles is supposed to have some sort of significance • takes into account magnitude of differences in the utilities of bundles

sublet

to have a person other than the original tenant take over the rental unit and payments for the remaining term of the lease

levy

to impose a tax upon

bubble

trade in an asset at a price or price range that strongly exceeds the asset's intrinsic value; characterized by the rapid escalation of market value, particularly in the price of assets • typically, a market crash follow

feasible allocation

trades in which the collection of all good being traded is equal to the total amount of goods in a particular economy; condition in which the total amount of each good consumed is equal to the total amount available • x'a + x'b = w'a + a'b • x"a + x"b = w"a + a"b • EX: A mother distrubutes a pack of 20 M&Ms to her only two daughters. If one daughter has 13 M&Ms, then the other must have the other 7. • EX: If there are 10 units of good 1 and 20 units of good 2, then if A holds (7, 12), B must be holding (3, 8).

perfect substitutes

two goods for which the marginal rate of substitution of one for the other is a constant • linear line with a constant slope • The preferences for two goods that are perfect substitutes are strictly convex. • Marginal Rate of Substitution is constant at −1

perfect complements

two goods with right-angle indifference curves u(x1,x2) = min {ax1, bx2}

perfect substitutes

two products that are treated as identical products; two goods for which the marginal rate of substitution of one for the other is a constant • EX: u(x1, x2) = √(x1 + x2) • EX: v(x1,x 2) = 13x1 + 13x2

perfectly elastic supply

unique scenario in which vendors can supply any amount of a good at a constant price; the industry will supply any amount desired of the good at some given price and no units at any other price • Equilibrium price is determined by supply only • Equilibrium quantity is determined by demand only • totally horizontal supply curve • Equilibrium Supply Price = price of goods + taxes

fixed supply

unique scenario in which vendors can't change the amount of goods available for regardless of the price. • supply curve is perfectly vertical • Example: The same number of tickets will be available for a football match regardless of the price of the tickets. • equilibrium price is determined by demand only

tautology

unnecessary repetition

What is v(3) in terms of reservation prices?

v(3) - v(0) = r1 + r2 + r3

What is the difference between consumer's surplus and consumers' suplus?

• Consumer's Surplus : the consumer surplus of one consumer • Consumers' Surplus : the aggregated consumer surplus of a collection of consumers

What do the demand and supply prices measure?

• Demand Price: measures which price the consumer is willing to buy a good • Supply Price: measures which price the vendor is willing to supply a good

What is the effect of a subsidy in a market with a horizontal supply curve? With a vertical supply curve?

• Horizontal Supply Curve (a good is supplied at a constant price, regardless of quantity): A subsidy would essentially move the supply curve down to a lower price level, increasing the amount produced. • Vertical Supply Curve (a good is supplied at a constant quantity, regardless of price changes): A subsidy would still result in the same quantity produced, but buyers would pay less because of the subsidy. The entire subsidy gets passed along to the consumers if the supply curve is flat, but the subsidy is totally received by the producers when the supply curve is vertical.

Budget Line Equation (Numeraire Forms)

• Numeraire: an economic term that means a benchmark value that's used to compare the value of similar products or financial instruments

Quasilinear preferences Engel Curve

• Quasilinear preferences: "all indifference curves are shifted versions of one indifference curve" Increasing income doesn't change the demand for good 1 at all, and all the extra income goes entirely to the consumption of good 2. • EX: Initially Hal may spend my income only on pencils, but when my income gets large enough, he stop buying additional pencils—all of his extra income is spent on other goods.

Quasilinear preferences Income offer curve

• Quasilinear preferences: "all indifference curves are shifted versions of one indifference curve" • Quasilinear preferences utility function: u(x1, x2) = v(x1) + x2 Increasing income doesn't change the demand for good 1 at all, and all the extra income goes entirely to the consumption of good 2. • EX: Initially Hal may spend my income only on pencils, but when my income gets large enough, he stop buying additional pencils—all of his extra income is spent on other goods.

A Pareto efficient allocation that is not an equilibrium

• See diagram The pareto effeicent allocation among the two traders isn't at aquilibrium because A would be better off buying the bundle Y. • Y is a higher indifference curve for trader A and lies on the same budget line as X

Change in consumer's surplus

• The change in consumer's surplus is sum of the square area and the triangular area below p1. • rectangle: reduction in consumer surplus due to change in price (p2 - p1) only • triangle: reduction in consumer's surplus due to reduction in sales (the consumer buys less of good x since it's more expensive) The change in consumer's surplus associated with a price change has a roughly trapezoidal shape. It can be interpreted as the change in utility associated with the price change.

Cobb-Douglas Preferences

• c: a • d: a - 1 • x1: demand for good 1 • p: price of a good • x1 = am / p1 For a fixed value of p1, this is a linear function of m. Thus doubling m will double demand, tripling m will triple demand, and so on. • x2 = (1 - a) m / p2

Why is it that a perfectly discriminating monopolist can be Pareto efficient within the Edgeworth box?

• discriminating monopolist: monopolist that sells identical products for different prices, with the intention of selling each product at the highest price a particular customer is willing to pay Because each selling price remains on the indifference curve of the customers. • See attached diagram

Indifference Curves Video Link

• https://youtu.be/iOmDo5jLFw8

perfect substitutes function

• m = - a / b

For arbitrary prices (p1, p2) there is no guarantee that supply will equal demand—in either gross demand or net demand. Why is this so?

• net demand: because the amount that A wants to buy (or sell) will not necessarily equal the amount that B wants to sell (or buy). • gross demand: because the total amount that the two agents want hold of the goods is not equal to the total amount of that goods available In other words, the market could be at a disequilibrium.

perfect complements Engel curve

• the attached graphs represents the demand behavior of perfect complements • the Engel curve is the diagonal line through the origin (because the consumer will always consume the same amount of each good)

perfect complements Income offer curve

• the attached graphs represents the demand behavior of perfect complements • the income offer curve is the diagonal line through the origin (because the consumer will always consume the same amount of each good)

perfect substitutes income offer curve

• the attached graphs represents the demand behavior of perfect substitutes

How can it be expressed in an algebra expresssion that in equilibrium the total demand for each good should be equal to the total supplyequilibrium the total demand for each good should be equal to the total supply?

• x'A (p1, p2) + x'B (p1, p2) = w'A + w'B • x"A (p1, p2) + x"B (p1, p2) = w"A + w"B KEY • A: trader A • B: trader B • w: initial endowment • p: price • x': good #1 • x": good #2 Another way to describe that: • [x'A (p1, p2) -w'A] + [x'B (p1, p2) - w'B] = 0 • [x"A (p1, p2) -w"] + [x"B (p1, p2) - w"B] = 0

perfect complements demand curve

• x: quantity of good • p: price of good

perfect complements price offer curve

• x: quantity of good • p: price of good

perfect substitutes demand curve

• x: quantity of good • p: price of good

perfect substitutes price offer curve

• x: quantity of good • p: price of good