Econ 311
4 Factors that influence Supply
(1) price (2) suppliers' costs of production (3) number of sellers (4) sellers' outside options
Inelastic (E<1)
Elasticities with magnitude lass than 1 are referred to as inelastic.
Using calculus to calculate the MRS when starting with the Utility function
Take the consumer who has utility for goods X and Y, U(X,Y). Any of the consumer's indifference curves show how the consumer trades off good X for good Y while keeping utility constant. We can choose any one of these indifference curves and call its level of utility
Solving unconstrained optimization problem using calculus
Take the partial derivatives of the objective function with respect to each of the variables, set them equal to zero, and solve for the variables.
Marginal Rate of Substitution (MRS)
The marginal rate of substitution measures the willingness of a consumer to trade one good for the other. It is measured as the negative slope of the indifference curve at any point. To find the slope at any point on the indifference curve you find the slope of the tangent line = instantaneous rate of change MRS sub XY = MU X / MU Y = derivate for x while treating y as a constant / derivative for y while treating y as a constant. Ex: At point A, the slope of the curve is -2, meaning that the MRS is 2. This implies that, for that given bundle, Sarah is willing to trade 2 burritos to receive 1 more latte. At point B, the slope is -0.5 and the MRS is 0.5. At this point, Sarah is only willing to give up 0.5 burritos to get another latte.
Implication of Utility maximization
The marginal-utility-ratio-equals-price-ratio result has another implication for the economy as a whole that can initially be surprising. Even if two consumers have very different preferences between two goods, they will have the same ratio of marginal utilities for the two goods, because utility maximization implies that MRS equals the ratio of the prices.
Market Demand
The market demand for a good is the sum of all the individual demand curves for it. That is, the market quantity demanded for a good at a particular price is the sum of every individual consumer's quantity demanded at that price. - a market demand curve will never be to the left of any individual demand curve, because all consumers combined must consume at least as much of a good at a given price as any single consumer does. For a similar reason, the slope of the market demand curve must also be as flat as, or flatter than, any of the individual demand curves. That is, for a given change in price, the change in quantity demanded for the market as a whole must be at least as great as the change in quantity demanded by any individual consumer.8 Finally, if the price is so high that only one consumer wants any of the good, the individual demand curve for that consumer will lie directly on top of the market demand curve at that price. At that point, the consumer is the market.
A change in the price of a substitute good
The more alike two goods are, the more one can be substituted for the other, and the more responsive the increase in quantity demanded of one will be to price increases in the other. - Changes in the prices of a good's substitutes lead to shifts in the good's demand curve. When a substitute for a good becomes more expensive, this raises the quantity demanded of that good at any given price level. As a result, the demand curve for the good shifts out (the demand for that good increases). When a good's substitutes become cheaper, the quantity demanded at any given price falls, and the good's demand curve shifts in.
Income elasticity
The percent changed in the quantity consumed of a good in response to a 1% change in income
Demand Choke Price
The price at which quantity demanded equals zero
5 Factors that influence demand/quantity demanded: 1) Price
The price of a good is the most important consideration. Because for example few consumers would pay $40 per pound for tomatoes, but many would pay $1 a pound
Expected Values
The probability-weighted average payout. The expected value of any uncertain outcome is the sum of the product of each possible outcome/payment and the probability of that outcome/payment. (Equivalently, it is the probability-weighted average outcome.) where: p sub 1,2,..N= probability of payouts with N possible payments M sub 1,2,...N = each possible payment/outcome - The basic way to incorporate risk into NPV investment analysis is to compute NPV as an expected value, that is, by weighting each payoff by the probability that it happens. Any risky payout can be described as a combination of two things: the different payouts that could possibly happen, and the probability of each possible outcome occurring.
Relationship between price elasticity and linear demand and supply
The ratio between price and quantity (P/Q) and the magnitude of the elasticity of a demand curve decrease as we move down the curve. At point A, Q = 0, P/Q = ∞, and the price elasticity of demand is -∞. Between points A and B, the demand curve is elastic with a price elasticity of demand less than -1 (more than 1 in absolute value). At point B, the demand curve is unit elastic, or the price elasticity of demand equals -1. Between points B and C, the demand curve is inelastic with a price elasticity of demand greater than -1 (less than 1 in absolute value). At point C, P = 0, P/Q = 0, and the price elasticity of demand equals zero.
Size of Income Effect
The size of the income effect is related to the quantity of each good the consumer purchases before the price change. The more the consumer was spending on the good before the price change, the greater the fraction of the consumer's budget affected by the price change. A price drop of a good that the consumer is initially buying a lot of will leave him with more income left over than a price drop of a good with a small budget share (and a price increase will sap a greater share of the consumer's income)
Interest rate
Interest expressed as a fraction of the principal.
Solving constrained optimization problem using calculus whose utility is the standard cobb-douglas functional form
1. At the optimum, the marginal rate of substitution equals the ratio of the two goods' prices. First, take the partial derivatives of the utility function with respect to each of the goods to derive the marginal utilities 2. Next, use the relationship between the marginal utilities and the marginal rate of substitution to solve for MRS sub (XY) and simplify the expression: 3. Find Y as a function of X by setting MRS sub (XY) equal to the ratio of the prices 4. Now that we have the optimal relationship between Y and X, substitute the expression for Y into the budget constraint to solve for the optimal consumption bundle
4 general assumption that help consumers determine their preferences about all the possible combinations of goods and services they can buy
1. Completeness and Rankability 2. For most goods, more is better than less (or at least more is no worse than less) 3. Transitivity 4. The more a consumer has of a particular good, the less she is willing to give up of something else to get even more of that good
2 different ways two goods might be perfect substitutes
1. Different-sized packages of the same good 2. Another way perfect substitutes might arise is if there are attributes of a product that a particular consumer does not care at all about. For instance, some people might not care about whether a bottle of water is branded Aquafina or Dasani. Their indifference curves when comparing Aquafina and Dasani water would therefore be straight lines. On the other hand, other consumers who do care about such features would not view the goods as perfect substitutes, and their indifference curves would be curved.
5 Factors that influence demand/quantity demanded
1. Price 2. The Number of Consumers 3. Consumer Income or Wealth 4. Consumer Tastes 5. Prices of Other Goods
4 commonly assumed characteristics of indifference curves
1. We can always draw indifference curves 2. We can figure out which indifference curves have higher utility and why they slope downward 3. Indifference Curves never cross 4. Indifference curves are convex to the origin (The bend toward the origin in the middle)
4 Key Assumptions Regarding Competitive Demand/Supply Model
1. We restrict our focus to supply and Demand in a single market 2. All goods bought and sold in the market are identical 3. All goods sold in the market sell for the same price, and everyone has the same information 4. There are many producers and consumers in the market
Compounding interest
A calculation of interest based on the sum of the original principal and the interest paid over past periods.
5 Factors that influence demand/quantity demanded: 4) Consumer Tastes
A change in consumer preferences, for a given level of the consumer's income and product's prices will change the amount of a product the consumer wants to purchase. Taste changes can be driven by all sorts of forces. For example, news about the health benefits of eating tomatoes would make many consumers want to eat more of them. On the other hand, news about salmonella being found in some tomato crops will make consumers reluctant to purchase them. For other products, taste changes might arise due to a really popular advertising campaign, fads, changes in demographics, and so on.
Income expansion path
A curve that connects a consumer's optimal bundles at each income level. This curve always starts at the origin because when income is zero, the consumption of both goods must also be zero. Figure 5.3 shows Meredith's income expansion path for bus rides and bottled water. - When both goods are normal goods, the income expansion path will be positively sloped because consumption of both goods rises when income does. If the slope of the income expansion path is negative, then the quantity consumed of one of the goods falls with income while the other rises. The one whose quantity falls is an inferior good. Remember that whether a given good is normal or inferior can depend on the consumer's income level.
Engel Curve
A curve that shows the relationship between the quantity of a good consumed and a consumer's income. Create an engel curve for each good. - If the Engel curve has a positive slope, the good is a normal good at that income level. If the Engel curve has a negative slope, the good is an inferior good at that income.
Giffen Goods
A giffen good is a good for which price and quantity demanded are positively related. Which means, giffen goods are goods for which a fall in price leads the consumer consumer to want less of the good. - The more expensive a Giffen good is, the higher the quantity demanded. This happens because, for Giffen goods, the substitution effect of a price drop, which acts to increase the quantity a consumer demands of the good, is smaller than the reduction in the desired quantity caused by the income effect. Note that this means Giffen goods must be inferior goods. Ex: Figure 5.14 gives a graphical example. The two goods are potatoes and meat, and potatoes are the Giffen good. The utility-maximizing bundle at the original prices is shown at point A. When potatoes become cheaper, the budget constraint rotates out from BC1 to BC 2 and the optimal bundle shifts from A to B. Notice that in this case, the quantity of potatoes consumed at point B is smaller than the quantity consumed at A even though potatoes are now cheaper.
Inferior good
A good for which consumption decreases when income rises
indifference curve
A mathematical representation of the combination of all the different bundles of goods that give a consumer the same utility. The combination of all the different bundles of goods that give a consumer the same utility is called an indifference curve. - An especially good way of understanding utility is to take the special case in which a consumer is indifferent between bundles of goods; that is, each bundle provides the consumer with the same level of utility. - For each level of utility, there is a different indifference curve. Because we assume that more is preferred to less, an indifference curve lying to the right and above another indifference curve reflects a higher level of utility - Any indifference curve that is closer to the origin (zero units of both goods) than another curve has a lower utility (we learn below that they can't cross).
cross price elasticity of supply
A measure of the responsiveness of the quantity supplied of a good to changes in the price of a related good. the percentage change in the quantity supplied of one good divided by the percentage change in the price of another good.
Relationship between price elasticity and Slope of linear demand and supply curve.
A percentage change in quantity (%ΔQ) is the change in quantity (ΔQ) divided by the original quantity level Q. That is, %ΔQ = ΔQ/Q. Similarly, the percentage change in price is %ΔP = ΔP/P.
Interest
A periodic payment made by individuals or firms that depends on the value of the assets the interest payments are tied to
Income effect
A price shift changes the purchasing power of consumers' incomes—the amount of goods they can buy with a given dollar-level expenditure. If a good gets cheaper, for example, consumers are effectively richer and can buy more of the cheaper good and other goods. If a good's price increases, the purchasing power of consumers' incomes is reduced, and they can buy fewer goods. Economists refer to consumption changes resulting from this shift in spending power as the income effect. - The income effect is the change in quantities demanded due to the change in the consumer's purchasing power after the change in prices. When the price of basketball tickets decreases, Carlos can afford to purchase a larger bundle than he could before the price change. The change in the quantity of goods consumed from bundle A′ to B represents the income effect.
Utility Function
A utility function summarizes the relationship between what consumers consume and their level of well-being. - Generally Utility is written as U= U(first alternative, second alternative) Ex: Formula using Kit Kats (K) and junior mints (J): U = U(K, J) In consumer behavior, the inputs to a utility function are the different things that can give a person utility. Examples of inputs to the utility function include traditional goods and services like cars, candy bars, health club memberships, and airplane rides. The output of the utility function is the consumer's utility level. By mapping the bundles a consumer considers to measures of the consumer's level of well-being—this bundle provides so much utility, that bundle provides so much utility, and so on—a utility function gives us a concise way to rank a consumer's bundles.
5 Factors that influence demand/quantity demanded: 2) The Number of Consumers
All else equal, the more people there are in a market, the greater the quantity of the good desired.
Changes in Quantity supplied
Analogous to demand curves, the changes in a good's price when everything else stays constant lead to changes in quantity supplied, movements along a supply curve.
5 Factors that influence demand/quantity demanded: 3) Consumer Income or Wealth
As a consumer becomes richer, she will buy more of most goods. Tomatoes (and clothes and cars and jewelry and porterhouse steaks) probably fall in that category for most people. Sometimes, however, when a consumer becomes richer, she buys less of a good. For example, she might buy a car and stop taking public transportation and might stay in nice hotels instead of youth hostels. The consumption of these goods still responds to income or wealth, but in a different direction.
Effects of demand/supply shifts on market equilibrium
As we have learned, demand and supply curves hold constant everything else besides price that might affect quantities demanded and supplied. If any other factor changes, there will be a new market equilibrium because either the demand or supply curve or both curves will have shifted. Ex: After a salmonella outbreak, the demand for tomatoes decreases, causing a leftward shift of the demand curve from D1 to D2. This fall in demand results in a new equilibrium point E2, which is lower than the initial equilibrium point E1. The equilibrium quantity falls from Q1 (400 pounds) to Q2 (150 pounds), and the equilibrium price falls from P1 ($3) to P2 ($1.75).
Relationship between price elasticity and linear supply
Because the slope of the curve is constant, the changes in elasticity along the curve are driven by the price-to-quantity ratio. For the smallest increase in price, the quantity supplied rises from zero to a positive number, an infinite percentage change in quantity supplied. The ratio between price and quantity (P/Q) and the magnitude of the elasticity of a supply curve decrease as we move up the curve. At point A, Q = 0, P/Q = ∞, and the price elasticity of supply is ∞. From B to C to D, the decrease in P/Q is reflected in the decrease of the slopes of the rays from these points to the origin. Unlike the demand curve, the price elasticity of supply will never reach zero because the supply curve never intercepts the quantity axis.
MRS sub XY
Because we're moving along an indifference curve (so utility is constant at every point on it), the total change in utility from the move must be zero. So if you set the equation to zero, The MRSXY between two goods at any point on an indifference curve equals the inverse ratio of those two goods' marginal utilities:
Change in Supply
Changes in any other factors that influence supply change the quantity supplied at any given price and create shifts in the supply, which is called a change in supply.
Changes in Quantity Demanded
Changes in quantity demanded is a change along the demand curve and only occurs when the price of the good changes. A given demand curve such as D1 in Figure 2.1, illustrates how the quantity demanded of a good changes as its price and only its price changes.
Utility
Describes how satisfied a consumer is. For practical purposes, you can think of utility as a fancy word for happiness or well-being. It is important to realize that utility is not a measure of how rich a consumer is. Income may affect utility, but it is just one of many factors that do so.
Normal good
Economists call a good for which consumption rises when income rises, that is, a good for which the income effect is positive
slope of indifference curve
Economists have a particular name for the slope of an indifference curve: The Marginal rate of substitution of X for Y (MRS sub XY). This is the rate at which a consumer is willing to trade off or substitute exactly 1 unit of good X (the good on the horizontal axis) for more of good Y (the good on the vertical axis) and feel well off. - Indifference curves are all about tradeoffs: how much of one good a consumer will give up to get a little bit more of another good. The slope of the indifference curve captures this tradeoff idea exactly. Description of picture: In words, this means that in return for 1 more latte, Sarah is willing to give up 2 burritos. At point B, the marginal rate of substitution is 0.5, which implies that Sarah would sacrifice only half of a burrito for 1 more latte (or equivalently, she would sacrifice 1 burrito for 2 lattes)
Elastic (E>1)
Elasticities with magnitudes (in absolute value) greater than 1 are referred to as elastic.
Relationship with Demand/Supply slope and the size of the equilibrium shift
Even for a fixed-size demand or supply curve shift, the magnitudes of the resulting equilibrium price and quantity changes can vary. Specifically, the relative sizes of the price and quantity changes depend on the steepness of the demand and supply curves. If the demand curve shifts, then the slope of the supply curve determines whether the shift leads to a relatively large equilibrium price change and a relatively small equilibrium quantity change, or vice versa. If the supply curve shifts, it's the slope of the demand curve that matters. Steeper curves mean that price changes are correlated with relatively small quantity changes. When demand curves are steep, this implies that consumers are not very price-sensitive and won't change their quantity demanded much in response to price changes. Similarly, steep supply curves mean that producers' quantities supplied are not particularly sensitive to price changes. Flatter demand or supply curves, on the other hand, imply that price changes are associated with large quantity changes. Markets with flat demand curves have consumers whose quantities demanded change a lot as price varies. Markets with flat supply curves will see big movements in quantity supplied as prices change.
4 Factors that influence Supply: 4) Sellers' Outside options
Farmers who are busy selling tomatoes at Pike Place Market aren't selling some other product or selling tomatoes at some other place. A change in farmers' prospects for doing business in markets for other goods or in other markets for tomatoes can affect their willingness to supply tomatoes at Pike Place Market. These prospects depend on factors such as the prices of other goods the farmers might be growing and selling (radishes, peppers, or green beans) or tomato prices at markets other than Pike Place Market.
When the income expansion path or Engel curves are more useful for understanding the effect of income on consumption choices
If we care about how the relative quantities of the two goods change with income, the income expansion path is more useful because it shows both quantities at the same time. On the other hand, if we want to investigate the impact of income changes on the consumption of each particular good, the Engel curve is best because it isolates this relationship more clearly. The two curves contain the same information but display it in different ways due to the limitations imposed by having only two axes.
Example of perfect substitutes
Figure 4.9 shows an example of two goods that might be perfect substitutes: 12-ounce bags of tortilla chips and 3-ounce bags of tortilla chips. If all the consumer cares about is the total amount of chips, then she is just as well off trading 4 small bags of chips for each large bag, regardless of how many of either she already has. These kinds of preferences produce linear indifference curves, and utility functions for perfect substitutes take on the general form U= aX + bY, where a indicates the marginal utility of consuming one more unit of X and b indicates the marginal utility of consuming one more unit of Y. This is precisely the situation shown in Figure 4.9. The indifference curves are straight lines with a constant slope equal to -1/4, which means that the MRSXY is also constant and equal to 1/4. We can't actually say what values a and b take here, only that their ratio is 1 to 4—that is, a/b = 1/4. The indifference curves in the figure would be the same if a = 1 and b = 4 or if a = 40 and b = 160, for instance. This is another demonstration of the point we made above: A transformation of a utility function that does not change the order of which goods the consumer prefers implies the same preference choices.
slope of a curve
First, the slope of a curve, unlike a straight line, depends on where on the curve you are measuring the slope. To measure the slope of a curve at any point, draw a straight line that just touches the curve (but does not pass through it) at that point but nowhere else. This point where the line (called a tangent) touches the curve is called a tangency point. The slope of the line is the slope of the curve at the tangency point.
4 general assumption that help consumers determine their preferences: 3. Transitivity
For any three bundles of goods (call them A, B, and C), if a consumer prefers A to B and also prefers B to C, then she prefers A to C. If you prefer apples to oranges, and you prefer oranges to bananas, then transitivity implies that you must also prefer an apple to a banana. Note that, as always, we are holding everything else constant when making these comparisons. Transitivity does not mean that you prefer apples to bananas in all situations, only that, at a given moment, you prefer apples to bananas. Transitivity imposes logical consistency on the preferences.
Calculation of Present discounted value
Formula: (V sub t) / (1+r)^t Where: V sub t = Future payment that needs to be expressed in present-value t = number of periods payment occurs in the future r = the interest rate - First, PDVs are proportional to the future value being discounted. If Vt were twice as high, its PDV would be, too. - Second, just as we noted above, higher interest rates imply lower PDVs for fixed values of Vt and t. The intuition is that higher interest rates reduce the initial value necessary to grow to future value Vt - the PDV of any particular value Vt is smaller the further into the future that it occurs. The PDV of $104 one year from now is greater than the PDV of $104 in two years, which is itself greater than the PDV of $104 three years from now, and so on.
Rule of 72
Formula: Doubling time = per-period interest rate / 72 There's a handy rule-of-thumb for approximating how long it will take for a balance growing at any constant interest rate to double. It's referred to as the "Rule of 72." To use it, simply divide 72 by the per-period interest rate. The quotient will be the approximate number of periods until the balance doubles.
The degree of Risk Aversion
Given the connection between diminishing marginal utility of income (reflected in how curved the utility-income relationship is) and risk aversion, it should be clear that the greater the curve in a consumer's utility function, the more risk-averse he is.
Complements
Goods that are often purchased and used in combination with a certain good. A price decrease in a good's complement will cause consumers to want more of the good
5 Factors that influence demand/quantity demanded: Prices of Other Goods
Goods that can be used in place of another good are called substitutes. When the price of a substitute good falls, consumers will want to buy more of it and less of the initial good. We can also think of the same good in a different market as a substitute good. Goods that are often purchased and used in combination with a certain good are called complements. When the price of a complement falls, consumers will want to buy more of it and also more of the initial good. The prices of substitutes and complements both affect how much of a good consumers want to buy, but they have opposite effects. A price decrease in a good's substitute will cause consumers to want less of the good; a price decrease in a good's complement will cause consumers to want more of the good. The prices of substitutes and complements both affect how much of a good consumers want to buy, but they have opposite effects. A price decrease in a good's substitute will cause consumers to want less of the good; a price decrease in a good's complement will cause consumers to want more of the good.
Substitutes
Goods that can be used in place of another good. A price decrease in a good's substitute will cause consumers to want less of the good
risk loving utility function
If it curves up (which can happen), then we say that person is risk-loving. A risk-lover would actually pay money to have a chance to gamble on a big payoff rather than take the certainty equivalent.
Excess supply in equilibrium
If the current price is higher than the equilibrium price, there will be excess supply. Over time, price will fall and the market will move toward equilibrium
Excess Demand in equilibrium
If the current price is lower than the equilibrium price, there will be excess Demand. Over time, price will rise and the market will move toward equilibrium
risk neutral utility function
If the curve stays straight, we call the consumers risk-neutral.
Unit Elastic
If the price elasticity of demand is exactly -1, or the price elasticity of supply is exactly 1, this is referred to as unit elastic.
Consumer's response to an increase in income when both goods are normal
If the prices of vacations and basketball tickets remain unchanged, an increase in Evan's income means that he can afford more of both goods. As a result, the increase in income induces a parallel, outward shift in the budget constraint from BC1 to BC2. Note that, because we hold prices fixed, the slope of the budget constraint (the ratio of the goods' prices) remains fixed. The new optimal consumption bundle at this higher income level is B, the point where indifference curve U2 is tangent to BC2.
Using Algebra to move from individual to market demand
If we plug in the prices from Figure 5.19, they match the quantities in the figure as long as we are on the part of the curve labeled A in Figure 5.19 where quantities demanded by both you and your cousin are above zero. According to the equation, market demand when P = $40 is Qmarket = 6, which is what the figure shows, and when P = $20, Qmarket = 12, just as on the figure. We're not quite done yet, though. The prices at which you and your cousin will consume no speakers—the demand choke prices—are different. Yours is $100; your cousin's is $52. (You can check this by plugging these prices into the demand curves and verifying that the quantities demanded equal zero.) That means at prices above $52, the market demand is only your demand because your cousin's quantity demanded is zero. There is no negative demand allowed. This isn't accounted for when we add together the two demand curves above, however, because at prices above $52, the part of the market demand curve coming from the formula for Q cousin is less than zero. Therefore, market demand is your demand, Q = 5 - 0.05p, for prices between $52 and $100 (quantity demanded is zero at prices higher than $100), and is Q = 18 - 0.3P (yours plus your cousin's) for prices below $52. That is, the market demand has a kink at P = $52.
4 general assumption that help consumers determine their preferences: 2. For most goods, more is better than less (or at least more is no worse than less)
In general, more of a good thing is good. If we like a car that is safe in a crash, we would like that same car even better if it were even safer.
Mathematical formula for budget constraint
Income = P sub X Q sub X + P sub Y Q sub Y Where: P sub X & P sub Y = The prices of 1 unit of goods X and Y Q sub X & Q sub Y = The quantities of the goods The equation simply says that the total expenditure on the two goods (the per-unit price of each good multiplied by the number of units purchased) equals the consumer's total income.
Another way to rewrite the optimization condition in terms of the consumer's marginal utility per dollar spent
It is often helpful to rewrite this optimization condition in terms of the consumer's marginal utility per dollar spent.
Solving Consumer's Choice Optimization Problem Mathematically
Mathematically, the tangency of the indifference curve and budget constraint means that they have the same slope at the optimal consumption bundle. Slope of indifference curve (-MRS sub XY) = Slope of budget constraint (-P sub x / P sub y) - Therefore, the fact that the consumer's utility-maximizing bundle is at a tangency between an indifference curve and the budget constraint gives us this key insight: When the consumer spends all her income and maximizes her utility, her optimal consumption bundle is the one at which the ratio of the goods' marginal utilities exactly equals the ratio of their prices.
4 Factors that influence Supply: 3) The number of sellers
More suppliers supplying a good to a market will raise the available supply
Deriving market demand curves from individual demand curves
Moving from individual demand curves to market demand is conceptually fairly simple. There's just one thing you have to be careful about. Market demand curves are derived by adding quantities of individual demand curves, not prices. That is, individual demands are graphically added horizontally, not vertically. When you add horizontally, you are summing up all the individual quantities demanded, holding price fixed. This is exactly what you want to do because market demand is the total quantity demanded at any given price. If you add individual demand curves vertically, however, you are holding quantities demanded fixed while adding up the prices. That's a very different conceptual exercise and one that, in this case at least, doesn't really make any sense. Likewise, if you are combining individual demand curves algebraically rather than graphically, make sure you've written out the individual demand curves as quantities demanded as a function of price. When you add those equations, you'll just be adding the quantities, which is again what you want to do. If you instead try to add equations where prices are a function of quantities (economists call these "inverse demand curves"), again you'll be doing the very different exercise of adding up prices across individuals while holding the quantities fixed.
Example of Risk-averse person
Notice another important thing about point C: It's at an expected utility level, 8, that is below Adam's utility function at that same income level. According to Adam's utility function, an income level of $68,000 allows him to achieve a utility of U=√68=8.25, as shown at point D in Figure 14.3. What this means is that the same expected income, $68,000, can give Adam different levels of expected utility depending on the riskiness of the underlying income levels on which the expectation is based. Due to the chance of tornado, Adam's income is uncertain, and his $68,000 in expected income delivers an expected utility of 8. But, if his income is guaranteed to be $68,000, even though his expected income of $68,000has not changed, his expected utility would be 8.25. In other words, the very uncertainty about what his income will be reduces Adam's expected utility.
Example of Expected Income & Utility
Now suppose that Adam's income is $100,000 in a year there is no tornado and only $36,000 if there is a tornado. The utility levels corresponding to these incomes are shown as poin as B and A, respectively, in Figure 14.3. With $100,000 in income, Adam's utility is U=√100=10; with $36,000 in income, it's U=√36=6. Let's say the probability of a tornado is ridiculously high, 50%, to make the math easy. This is where the uncertainty comes from. Following a basic expected value calculation, we first compute Adam's expected income for the year. There's a 50% chance his store blows down, giving him an income of $36,000. There's a 50% chance of no tornado, and his income is $100,000. Applying the formula for computing expected values, we find that Adam's expected income is $68,000
4 Factors that influence Supply: 1) Price
Price plays an important role in supply decisions. If farmers expect to be able to sell tomatoes at $40 a pound at Pike Place Market, the market will be loaded with them. The farmers will grow more tomatoes and choose to sell them at Pike Place Market rather than other outlets. If they expect the price to be only $1 per pound, there will be a much smaller quantity available for sale.
Mathematical Representation of Supply Curve
Q = 200P -200 Where: Q = Quantity supplied P = Is the price - This indicates that holding everything else constant, for every dollar increase in price, the quantity supplied of tomatoes increases by 200 pounds. For this supply curve, the supply choke price (the price at which quantity supplied equals zero) is $1. The inverse supply curve (price as a function of quantity supplied) is P = 0.005Q + 1.
Mathematics of Finding market equilibrium
Set Quantity Demanded = Quantity Supplied and solve P to find price equilibrium and then plug and solve
slope of budget constraint
Slope of budget constraint = (Quantity of item of vertical axis that could be bought if all income was spent on it) / (Quantity of item of Horizontal axis that could be bought if all income was spent on it) - The relative prices of the two goods determine the slope of the budget constraint. Because the consumer spends all her money when she is on the budget constraint line, if she wants to buy more of one good and stay within her budget, she has to buy less of the other. Relative prices pin down the rate at which purchases of the two goods can be traded off.
Factors that affect the budget constraint's slope/cause a shift
Slope: Because relative prices determine the slope of the budget constraint, changes in relative prices will change its slope. Shift: Income changes cause the budget constraint to shift. When income is reduced the constraint shifts in. When income is increased the constraint shifts outward
Risk-Averse
Suffering an expected utility loss from uncertainty, or equivalently, being willing to pay to have that risk reduced. - If a person prefers having a guaranteed amount to having a risky but equivalent-in-expected-value amount, we say the person is risk-averse. Uncertainty reduces the utility of a risk-averse person
4 Factors that influence Supply: 2) Suppliers' cost of production
Suppliers' production costs will change when input prices and production technology change. There are many inputs a supplier must use to produce tomatoes and bring them to market, including land, tomato seeds, harvesting equipment, or gasoline needed to ship tomatoes to markets, to name just a few. If the prices of these inputs change, the suppliers' costs will change and will influence the quantity of tomatoes supplied to the market. Similarly, changes in production technology, the processes used to make, distribute, and sell a good such as tomatoes, will change the costs of production. The more efficient these processes are, the lower the costs to sellers of providing tomatoes for sale. Lower costs will raise sellers' willingness to supply tomatoes at a particular price.
Relationship between risk and diminishing marginal utility
Suppose most of Adam's income comes from a country store he owns, and that the only important uncertainty his business faces is whether the store is destroyed by a tornado (causing Adam's income to take a big hit). We assume the utility, U, that Adam enjoys from goods purchased with his income is given by the function: U = sqrt(I) Where I = adam's income in thousand's of dollars
4 commonly assumed characteristics of indifference curves: 2. We can figure out which indifference curves have higher utility and why they slope downward
The "more is better" assumption implies that we can look at a set of indifference curves and figure out which ones represent higher utility levels. This can be done by holding the quantity of one good fixed and seeing which curves have larger quantities of the other good. This is exactly what we did when we looked at Figure 4.2. The assumption also implies that indifference curves never slope up. If they did slope up, this would mean that a consumer would be indifferent between a particular bundle and another bundle with more of both goods. There's no way this can be true if more is always better.
Principal
The amount of assets on which interest payments are made.
The income effect
The change in consumer's choices that results from change in the purchasing power of the consumer's income.
Consumer's choice optimization problems
The choice of how much to consume (like so many economic decisions) is a constrained optimization problem. There is something you want to maximize (utility, in this case), and there is something that limits how much of the good thing you can get (the budget constraint, in this case). - The quantity of some good is on the vertical axis, and the quantity of some other good is on the horizontal axis. This arrangement is extremely important, because it means we can display indifference curves and the budget constraint for two goods in the same graph, making the consumer's problem easier to solve.
Demand
The combined amount of a good that all consumers are willing to buy
Supply
The combined amount of a good that all producers in a market are willing to sell
risk premium
The compensation an individual would require to bear risk without suffering a loss in expected utility.
Elasticity
The concept of elasticity expresses the responsiveness of one value to changes in another and here specifically the responsiveness of quantities to prices. Elasticity relates the percent change in one value to the percent change in another. Ex: when we talk about the sensitivity of consumers' quantity demanded to price, we refer to the price elasticity of demand: the percentage change in quantity demanded resulting from a given percentage change in price.
Solving Consumer's Choice Optimization Problem graphically
The consumer's optimal consumption bundle occurs at the point of tangency between her budget constraint and her indifference curve, shown here at point A. The consumer can afford the consumption bundles represented by points B, C, and D, but these are on a lower indifference curve (U1 than is point A (U2). Point E is on a higher indifference curve (U3), but it lies outside the consumer's budget constraint and is thus infeasible. - Suppose an indifference curve and the budget constraint never touched. Then no point on the indifference curve is feasible, and by definition, no bundle on that indifference curve can be the way for a consumer to maximize her utility given her income. Now suppose the indifference curve crosses the budget constraint twice. This implies there must be a bundle that offers the consumer higher utility than any on this indifference curve and that the consumer can afford.
Marginal Utility
The extra utility a consumer receives from a 1-unit increase in consumption. Each good in a utility function has its own marginal utility. Computing MU using Calculus: Given a differentiable utility function: U(K, J):MU for J = derivate for J while treating K as a constant. MU for K = derivative for K while treating J as a constant
4 commonly assumed characteristics of indifference curves: 1. We can always draw indifference curves
The first assumption, completeness and rankability, means that we can always draw indifference curves: All bundles have a utility level, and we can rank them.
1. We restrict our focus to supply and Demand in a single market
The first simplifying assumption we make is to look at how supply and demand interact in just one market to determine how much of a good or service is sold and at what price it is sold. In focusing on one market, we won't ignore other markets completely—indeed, the interaction between the markets for different kinds of products is fundamental to supply and demand.
4 commonly assumed characteristics of indifference curves: 4. Indifference curves are convex to the origin (The bend toward the origin in the middle)
The fourth assumption of utility—the more you have of a particular good, the less you are willing to give up of something else to get even more of that good—implies something about the way indifference curves are curved. Specifically, it implies they will be convex to the origin; that is, they will bend in toward the origin as if it is tugging on the indifference curve, trying to pull it in.
An Example of the Income and Substitution Effects with an Inferior Good
The graph shows Judi's utility-maximizing bundles of steak and ramen noodles for two sets of prices. The optimal bundle at the original prices is shown at point A. The price of ramen noodles then drops, rotating the budget constraint outward. With the new budget constraint BC2, Judi can reach a higher level of utility U2 and chooses bundle B to maximize her utility.
Certainty Equivalent
The guaranteed income level at which an individual would receive the same expected utility level as from an uncertain income.
4 general assumption that help consumers determine their preferences: 4. The more a consumer has of a particular good, the less she is willing to give up of something else to get even more of that good
The idea behind this assumption is that consumers like variety. If you like birthday cake and haven't had cake lately, you might be willing to give up a lot for some cake. You might pay a high price for a cake, take the afternoon to bake a cake, or trade away your last carton of milk for some cake. On the other hand, if you've just polished off two-thirds of a cake, you are unlikely to be willing to pay much money for more, and you may very well want to trade the rest of the cake to get back some of that carton of milk.
Size of Substitution Effect
The size of the substitution effect depends on the degree of curvature of the indifference curves. - When indifference curves are highly curved, as in panel a, the MRS changes quickly as one moves along them. This means any given price change won't change consumption choices much, because one doesn't need to move far along the indifference curve to change the MRS to match the new relative prices. Thus, the substitution effect is small. When the indifference curve is less curved, the MRS does not change quickly along the curve. Thus, any given price change affects consumption choices more strongly. - Curvier Indifference Curve = Smaller substitution effect - Flatter indifference curve = Larger substitution effect
4 commonly assumed characteristics of indifference curves: 3. Indifference Curves never cross
The transitivity property implies that indifference curves for a given consumer can never cross.
Net Present Value (NPV) Analysis
The use of present discounted value to evaluate the expected long-term return on an investment. A method of evaluating investment projects that uses present discounted value to put all of an investment project's future cost and benefit flows on a common basis, so they can be compared apples-to-apples.
Present Discounted Value (PDV)
The value of a future payment in terms of equivalent present-period dollars. - a mathematical concept that allows us to compare costs and benefits over time in a way that puts all present and future financial values on equal footing. - Present discounted values use interest rates and compounding to compare payments happening at different times. The idea is to appropriately discount future values so that they can be put in terms of equivalent present-period dollars.
4 general assumption that help consumers determine their preferences: 1. Completeness and Rankability
This assumption implies that consumers can make comparisons across all sets of goods that they consider. Economists use the term consumption bundle (or just bundle) to describe any collection of these goods. The assumption means that, given any two bundles, a consumer can decide which she prefers (or whether she is indifferent, meaning she likes them the same). This assumption is important because it means that we can apply economic theory to any bundle of goods we want to discuss.
3. All goods sold in the market sell for the same price, and everyone has the same information
This assumption is a natural extension of the identical-goods assumption, but it also implies that there are no special deals for particular buyers and no quantity discounts. In addition, everyone knows what everyone else is paying.
4. There are many producers and consumers in the market
This assumption means that no one consumer or producer has a noticeable impact on anything that occurs in the market and on the price level in particular. This assumption also tends to be more easily justified for consumers than for producers.
Budget Constraint
This constraint describes the entire set of consumption bundles that a consumer can purchase by spending all of her money. Any combination of goods on or below the budget constraint (i.e., any point between the origin on the graph and the budget constraint, including those on the constraint itself) is feasible, meaning that the consumer can afford to buy the bundle with her income. Any points above or to the right of the budget line are infeasible. These bundles are beyond the consumer's reach even if she spends her entire income.
Total Effect
Total Effect = Substitution Effect + Income Effect - The total effect is the sum of the substitution and income effects. In this case, Carlos buys 1 more concert ticket and 2 more basketball tickets
Standard Cobbs-Douglas functional form
U(X,Y) = X ^(α)Y^(1 - α) When in this from indifference curves never hit the axes
2. All goods bought and sold in the market are identical
We assume that all the goods bought and sold in the market are homogeneous, meaning they are identical, so a consumer is just as happy with any one unit of the good (e.g., any gallon of gasoline). The kinds of products that best reflect this assumption are commodities, goods that are traded in markets where consumers view different varieties of the good as essentially interchangeable. Goods such as wheat, soybeans, crude oil, nails, gold, or #2 pencils are commodities. Custom-made jewelry, cars, the different offerings on a restaurant's menu, and wedding dresses are not commodities because the consumer typically cares a lot about specific varieties of these goods.
Equivalence between relative prices and slope of the budget constraint
We can see the equivalence between relative prices and the slope of the budget constraint by rearranging the budget constraint: The formula created at the bottom is the slope-intercept format of the budget constraint.
Calculation of Present discounted Value of Payment streams
We just saw how we can find the PDV of a payment that occurs at one particular moment in the future. It's easy to extend this method to payment streams—collections of payments that happen at different times. To compute the PDV of an entire stream, we just apply the present value discounting equation to each of the stream's elements and then add them together. Ex: Suppose you earn a scholarship that will pay you $1,000 in each of four installments: The first installment arrives today, and then the next three come one, two, and three years from today. The PDV of the scholarship is the sum of the PDVs of each installment. So, for any generic annual interest rate r, the scholarship's PDV is look to picture.
A risk-averse individual will pay to avoid risk
We plot the relationship between utility and income for a random guy named Adam in Figure 14.3. Adam's income is shown on the horizontal axis, and his utility from consuming the goods he buys with that income level is on the vertical axis. Utility rises with income, as we would expect, because the more income he has, the more stuff he can buy. However, the curve becomes less steep as his income rises. That is, Adam has diminishing marginal utility of income. The bump in utility he would enjoy from an increase in income of, say, $10,000 to $15,000 is more than the extra utility he'd experience from moving from an income of$1,000,000 to $1,005,000. It turns out that if diminishing marginal utility holds, Adam will be sensitive to risk and willing to pay to eliminate or reduce uncertainty.
The impact of Changes in another good's price: substitutes and complements
We start with a fixed level of income, a set of indifference curves representing the consumer's preferences, and initial prices for the two goods. We compute the optimal consumption bundle under those conditions. Then, we vary one of the prices, holding everything else constant. The only difference is that as we vary that price, we focus on how the quantity demanded of the other good changes.
3 steps to Computing Substitution and income affects from a price change
We start with the consumer at a point of maximum utility (Point A) where his indifference curve is tangent to his budget constraint. 1. When prices change, draw the new budget constraint (a price change rotates the budget constraint, altering its slope). Then find the optimal quantity at the point (Point B) where this new budget constraint is tangent to a new indifference curve. 2. Draw a new line that is parallel to the new budget constraint from Step 1 and tangent to the original indifference curve at Point A'. The movement along the original indifference curve from Point A (the original, pre-price change bundle) to this new tangency (point A') is the substitution effect. This movement shows how quantities change when relative prices change, even when the purchasing power of income is constant. 3. The income effect of the price change is seen in the movement from point A' to point B. Here, relative prices are held constant (the budget lines are parallel) but the purchasing power of income changes.
Consumer's Response to an increase in income when one good is inferior
When a good is inferior, an increase in a consumer's income decreases the consumer's consumption of that good. Here, mac and cheese is an inferior good, while steak is a normal good. When the consumer's income increases, shifting the budget constraint outward from BC1 to BC2, she consumes less mac and cheese and more steak at the optimal consumption bundle. From initial optimal consumption bundle A to her new optimal consumption bundle B, the quantity of mac and cheese consumed decreases from Qm to Q'm while her consumption of the normal good steak increases from Qs to Q's.?
Distinction between changes in quantity demanded and changes in demand
When a good's price changes but nothing else does, this change creates a movement along a fixed demand curve. Changes in any of the other factors that influence demand create shifts in the demand curve. In terminology, economists distinguish changes in quantity demanded, which happen when a change in a good's price creates movement along a given demand curve, from changes in demand, which happen when a good's entire demand curve shifts
Price elasticities and price responsiveness
When demand (supply) is very price-sensitive, a small change in price will lead to large changes in quantities demanded (supplied). That means the numerator of the elasticity expression, the percentage change in quantity, will be very large in magnitude compared to the percentage change in price in the denominator. For price elasticity of demand, the change in quantity will have the opposite sign as the price change, and the elasticity will be negative. But its magnitude (its absolute value) will be large if consumers are very responsive to price changes. - Markets with less price-responsive demand have elasticities that are small in magnitude. - Markets with large price elasticities of supply—where the quantity supplied is sensitive to price differences—would be those where it was easy for suppliers to vary their amount of production as price changes. - Markets with low price elasticities of supply have quantities supplied that are fairly unresponsive to price changes. This would occur in markets where it is costly for producers to vary their production levels, or it is difficult for producers to enter or exit the market.
Shifts in the Demand Curve
When one of the other (nonprice) factors that affect demand changes, the change affects the quantity of tomatoes consumers want to buy at every price which causes the demand curve to shift inward or outward. Ex: The demand curve D1 shifts with a change in any nonprice factor that affects demand. If tomatoes are suspected to be a source of salmonella, consumers will demand fewer tomatoes at any given price and the demand for tomatoes will shift inward, from D1 to D2. In contrast, if tomatoes are found to have cancer-fighting properties, the demand for tomatoes will shift outward, from D1 to D3.
Shifts in the supply curve
When one of the other (nonprice) factors that affect supply changes, the change affects the quantity of tomatoes that suppliers want to sell at every price. Ex: The supply curve S1 shifts when any nonprice factor that affects supply changes. If a faster harvesting method is developed, the supply of tomatoes will shift outward, from S1 to S2. In contrast, if there is a drought, the supply of tomatoes will shift inward, from S1 to S3. Similarly, if there is a drought, it will cost producers more to irrigate their fields. They will want to supply fewer tomatoes at any given price than they did before, and the supply will shift up and to the left,
Changes in the price of a complement good
When the price of a complement of a good increases, the quantity demanded of that good at every price decreases and its demand curve shifts in. If the price of a complement of a good falls, the quantity demanded of that good rises at all prices and the demand curve shifts out. Changes in the price of a complementary good shift the demand curve for the other good. Changes in a good's own price cause a move along the same demand curve.
Changes in the prices of substitutes or complements shift the demand curve
When the price of a substitute good rises or the price of a complement falls, the demand curve for good X shifts out. When the price of a substitute good falls or the price of a complement rises, the demand curve for good X shifts in.
Substitution Effect
When the price of one good changes relative to the price of another good, consumers will want to buy more of the good that has become relatively cheaper and less of the good that is now relatively more expensive. - The substitution effect is the change in quantities demanded due to the change in relative prices of basketball and concert tickets after the price of basketball tickets decreases. The budget constraint BC′ is parallel to Carlos's new budget constraint BC2 but tangent to his original utility level U1. The point of tangency between BC′ and U1, consumption bundle A′, is the bundle Carlos would purchase if relative prices changed but his purchasing power did not. The change from bundle A to bundle A' is the substitution effect.
perfect complements
When the utility a consumer receives from a good depends on its being used in fixed proportion with another good, the two goods are perfect complements. Perfect complements lead to distinctive L-shaped indifference curves. Mathematically, this can be represented as U = min{aX, bY}, where a and b are again numbers reflecting how consuming more units of X and Y affects utility. This mathematical structure means a consumer reaches a given utility level by consuming a minimum amount of each good X and Y. To be on the indifference curve U2, for instance, the consumer must have at least 2 left shoes and 2 right shoes. The kink in the indifference curve is the point at which she is consuming the minimum amount of each good at that utility level This L-shape is the most extreme case of curvature of indifference curves. It is at the other extreme from the straight-line indifference curves that arise with perfect substitutes, and its shape produces interesting results for MRSXY. At the horizontal part of the indifference curve, MRSXY equals zero, while on the vertical portion, the marginal rate of substitution is infinite.
Calculation of Net Present Value
Where: t = 0 is the current period and T is the last period in which any costs or benefits associated with the project occur. B sub 0, B sub 1, ..., B sub T = are the investment's benefits in the respective periods C sub 0, C sub 1, ..., C sub T = Are the costs
perfect substitutes
a good that a consumer can trade for another good, in fixed units, and receive the same level of utility.
Demand Curve
a graph of the relationship between the price of a good and the quantity demanded. A demand curve is drawn with the assumption that there is no change in any of the other factors—such as consumers' incomes, tastes, or the prices of other goods—that might also affect how much of a good consumers buy at any given price. Mathematical Representation of the Demand Curve for Figure 2.1: Q= 1000 - 200P Where: Q= Quantity Demanded (in pounds) Horizontal Axis P = the price (in dollars per pound) Vertical Axis
Supply Curve
a graph of the relationship between the price of a good and the quantity supplied. The supply curve in the figure slopes upward: Holding everything else equal, producers are willing to supply more of a good as price rises. Many firms experience increasing costs of production as their output rises. When this is the case, they need to earn a higher price in the market in order to induce them to produce more output. - A given supply curve such as S1 in Figure 2.3 illustrates how the quantity supplied of a good changes as its price, and only its price, changes.
cross-price elasticity of demand
a measure of how much the quantity demanded of one good responds to a change in the price of another good, computed as the percentage change in quantity demanded of the first good divided by the percentage change in the price of the second good.
market equilibrium
a situation in which quantity demanded equals quantity supplied. Graphically it is the point at which the Supply curve and demand curve intersect
indifference map
graph containing a set of indifference curves showing the market baskets among which a consumer is indifferent
Income Expansion path/ Engel curve for perfect compliments
ig. 7.6 shows the nature of a consumer's demand for perfect complements. Since the same amount each good will be consumed, the ICC will be a straight line through the origin with constant slope, as depicted by Fig. 7.6(a). Since the demand for x1 = m/(p1 + p2), the Engel curve is a straight line with of slope of p1 + p2 as shown in Fig. 7.6(b).
quantity demanded
the amount of a good that buyers are willing and able to purchase
Price elasticity of demand
the percentage change in quantity demanded resulting from a given percentage change in price. Formula: Price elasticity of demand = (% change in quantity demanded) / (% change in price) - First, because demand curves slope downward, the price elasticity of demand is always negative (or more precisely, always nonpositive; in special cases that we discuss later, it can be zero). Second, because it is a ratio, a price elasticity can also be thought of as the percentage change in quantity demanded for a 1% increase in price. That is, for this good, a 1% increase in price leads to a -2.5% change in quantity demanded.
Price elasticity of Supply
the percentage change in quantity supplied resulting from a given percentage change in price. Formula: Price elasticity of supply = (% change in quantity supplied) / (% change in price) - The price elasticity of supply is always positive (or again more precisely, always nonnegative) because quantity supplied increases when a good's price rises. And just as with demand elasticities, supply elasticities can be thought of as the percentage change in quantity in response to a 1% increase in price.