Exam 1
Suppose MRS is that 2 cokes are equivalent to one Jolt (for caffeine content). Jolt sells for $1 and coke for $0.75. For a budget of $15, what is the optimal consumption bundle of coke and jolt? -What is the new optimal bundle if the price of Jolt doubles from $1 to $2? -How much income is needed to compensate for the increased price of jolt in order to have the same caffeine intake as before? (15 caffeine)
(a) Budget constraint, PsS + PfF = M (but swap s for coke, etc): PcC + PjJ = M 0.75C + 1J = 15 Max coke M/Pc 15 / 0.75 = 20 Max jolt M/Pj 15 / 1 = 15 Slope = -Pj/Pc 1/0.75 = -1.33 So, 1.33 cokes must be given up to afford a jolt -The indifference curve is a straight line because they're perfect substitutes. -Because it takes 2 cokes to equal the caffeine in 1 jolt, 15 jolts will yield the same satisfaction as 30 cokes. Thus, a corner solution will be made and the consumer will choose to buy 15 jolts and no cokes; since they could only buy 20 cokes (which is less caffeine than the 15 jolt equivalent for the price). (b) New Slope = -Pj/Pc; -2/0.75 = 2.67 New budget constraint: 0.75C + 2J = 15, or, C=20-2.67J Max coke = 20 Max jolt: 15 / 2 = 7.5 But, the coke is only half the caffeine jolt is, so 20 cokes are equal to 10 caffeine. This is still more than the 7.5 caffeine from jolts; thus, coke at 20 has more caffeine so the consumer would choose a corner solution and get only coke. (c) Given that coke is now the most cost effective way to consume caffeine (corner solution); it would take 30 cokes to reach 15 caffeine, at $0.75 per coke, that's $22.5, or, a $7.5 increase in income. 15 / 0.5 = 30 0.75 x 30 = 22.5 22.5 - 15 = $7.5 increase in income
Suppose you receive M1 of your income in the 1st period and M2 in the second, and can earn interest r. (a) What is the most you can consume in the future period? (b) What is the most you can consume in the current period? (c) Ex: If M2 were $110,000 and the interest rate were 10%, find the present value of M2
(a) In order to consume the most in the future, you would have to set aside all of your current income, M1, which would gain interest r; becoming M1 (1+r). This would be combined with your future income for: M1(1+r) + M2 (b) The most you could consume in the current period is your current income plus the amount you can borrow against your future income, which is called the present value of M2. Denoted PV (M2). It is the amount that, if deposited today at the interest rate r, would be worth exactly M2 in the future period. We can find the present value of M2 by solving for PV(M2) in this equation PV(M2)(1+r) = M2; thus, we get: PV(M2) = M2/(1+r) -Present value formula: X / (1+r)^T where r is interest, T is time, and X is dollars (c) Using PV(M2) = M2/(1+r) we get: PVM2=110,000/(1+0.10) gives us: 100,000. Remember M2 is the future amount. Thus, 100,000 today will be worth 110,000 in the future at 10% interest -Current consumption has a higher price than future consumption because of the opportunity cost -The horizontal intercept of the intertemporal budget constraint is called the present value of lifetime income
Suppose Elena considers tea and coffee to be perfect substitutes and spends $12 on these 2 beverages. Coffee costs $1 and tea costs $1.20. (a) What is the initial demand for the 2 goods? (b) What will be the income and substitution effects of an increase in the price of coffee to $1.50?
(a) Initial demand is 12 cups of coffee and no tea (b) Because the price of coffee has risen to above the price for tea, she will now buy only tea. 12/1.20 = 10. In order to afford 12 cups of tea (point C) she would need a budget of $14.40, which she would like just as much as the original 12 cups of coffee. -With perfect substitutes the substitution effect can be very large
Example: The market demand curve for bus rides in a small community is given by P=100-(Q/10), where P is the fare per ride in cents and Q is the number of rides each day. (a) If the price of 50cents/ride, how much revenue will be collected each day? (b) What is the price elasticity demand for rides? (c) If they need more revenue, should they raise or lower the price? (d) How would your answers be different if the initial price had been 75 cents instead of 50?
(a) P=100-(Q/10), solve for Q=1,000-10P when P=50, Q=1,000-(10x50); thus, Q=500 Total revenue: 500x0.5 = $250 (b) ε = (P/Q) x (1/slope) (50/500) x (-10) = -1 for our elasticity The slope is from our original equation, P=100-(Q/10) (c) -1 puts the price elasticity at unity, where total revenue has attained its maximum value. If they raise or lower their price they will learn less. (d) At 75 cents, Total revenue Q=1,000-10P Q=1,000-10(75) Q = 250 At Q=250, total revenue: 250 x 0.75 = 187.5 Price Elasticity ε = (P/Q) x (1/slope) (75/250) x (-10) = -3 To earn more they would need to lower the price (we can figure that out by plugging in a value higher/lower in place of 75 and seeing if our price elasticity goes closer to -1 or not)
Suppose skis and bindings are perfect complements and Fatima spends all of her budget of $1,200 on them. Skis and bindings each cost $200 (a) How many of each will she buy? (b) What will be the income and substitution effects of an increase in the price of bindings to $400?
(a) Since they're perfect complements, the # of skis & bindings must be equal. Thus, 1,200 / 200 = 6. So, she'll buy 3 of each. Our optimal bundle is A. The max she could buy of each is 6 & 6. (b) The max she could buy of each is 6 skis & 3 bindings. (1200/400=3, &, 1200/200=6). We get a new optimal budget of D. Here, she buys 2 skis and 2 bindings. -Because they're perfect complements skis must still equal bindings (B=S). Thus, 400B+200S=1200, SO, 400S+200S=1200, solving for S=2 A budget of $1,800 is needed to attain the same indifference curve as before the price increase. With this new budget we could once again buy 3 of each, getting back to optimal bundle A. -For perfect complements, the substitution effect is zero. So, the total effect of the price increase is the same as the income effect of the price increase.
Free markets and the poor (price ceilings & price supports/floors)
- Efficiency says that given the low incomes of the poor, free exchange enables them to do the best they can. They can choose and get the best deals they can - Price ceilings attempting to make goods more affordable can make items less available. Ex: As price rises so too does the supply; so, if you put a cap on the price then you're capping the supply as well. - The government creates a price support / price floor, which means a product can't be sold for less than X. X is usually above equilibrium. This creates a surplus. Thus, price supports cause excess supply that the government usually has to buy.
Chapter 4
-Effects of changes in price and income -Income and substitution effects of a price change -Aggregating individual demand curves into market demand -Price and cross elasticities of demand -Elasticity and total expenditure -The dependence of market demand on income
An individual's demand curve for gas is given by P = 10 - Q, where P is the price of gas and Q is the quantity consumed. If the individual's weekly income is $1,000 and the current price of gas is $2, by how much will her consumer surplus decline if an oil import restriction raises the price to $3/gal?
-Our end points are 10 to 10 P=10-Q; 2=10-Q; thus, Q=8 -So, at a price of $2 (P=2) she will buy 8 gas P=10-Q; 3=10-Q; thus, Q=7 -So, at a price of $3 (P=3) she will buy 7 gas Our consumer surplus is a triangle. Recall that area of a triangle is (1/2) (base x height) -Thus, (1/2) (8 x 8) = $32. This is our consumer surplus at a price of $2. -Our consumer surplus at a price of $3: (1/2)(7 x 7) = $24.5 -Thus, the affect of the price change is a decrease in consumer surplus of 32 - 24.5 = $7.5
Budget constraints involving more than 2 goods
-With only 2 goods the budget constraint is a straight line; however, when there are more than 3 goods, the budget constraint becomes a hyperplane, or multidimensional plane.
Intertemporal Budget Constraint
-Your extreme points will involve fully consuming X in either the current or the future period. In the graph, we can invest our money for future gains of %20. Thus, if we consume all our money in the current period (C1) we will earn 0 in the future; alternatively if we consume no money in the current and fully invest it we will maximize future earnings at %20 interest for 120,000.
Learning Objectives
1.) Explain how the demand and supply curves summarize the behaviors of buyers and sellers. 2.) Explain why the equilibrium in a market identifies a price-quantity pair for which buyers and sellers are satisfied. 3.) Explain how shifts in supply and demand curves cause equilibrium prices and quantities to change 4.) Explain why transactions can always be found that make some parties better off without harming others whenever a market is not in equilibrium 5.) Explain why attempts to peg prices below or above their equilibrium levels produces negative side-effects and describe both the rationing and allocative functions of prices. 6.) List some determinants of supply and demand. 7.) Solve for equilibrium prices and quantities when supply and demand curves are expressed in algebraic form.
Factors that shift supply schedules -Improved technology -Higher wages -Lower interest rates -Higher prices for raw materials -Increase in number of firms -Expectation of higher prices -Good weather -Bad weather
1.) Increase in supply 2.) Decreases supply bad weather decreases supply
Determinants of Supply
1.) Technology 2.) Factor Prices 3.) The Number of Suppliers 4.) Expectations 5.) Weather - ex: ag crop affected by rain.
Application: The welfare effects of changes in housing prices Consider the following two scenarios; (for both of these your original wealth was $400,000) 1.) You have just purchased a house for $200,000. The very next day, the prices of all houses, including the one you just bought, double. 2.) You have just purchased a house for $200,000. The very next day, the prices of all houses, including the one you just bought, fall by half. -In each case, how does the price change affect your welfare?
1.) You're better off if it doubles, because your total wealth has increased from 400,000 to $600,000. Although your max housing has decreased, you can still buy the same bundle as before (A). But, bundle C has now become the best affordable bundle because you can spend more of your increased wealth on composite goods. 2.) Now, your max wealth is $300,000. So, you have less to spend on other goods; but, you can now buy 3 units of housing. The new best affordable bundle is labeled D. Here, you purchase more housing but less other goods. -Since your original bundle lies on the new budget constraints for both 1 & 2, you can't be worse off. The shifting indifference curves makes it possible in both scenarios to achieve a better outcome; thus, both are beneficial.
Market
A Market consists of the buyers and sellers of a good or service
The Income and Substitution effects of a change in price
A change in price has 2 effects, 1.) Substitution effect - When the price of a good rises, close substitutes become more attractive. Ex: when the price of coke rises, pepsi becomes more attractive. This is called the substitution effect of a price increase -The substitution effect always causes the quantity purchased to move in the opposite direction of the change in price (price ↑, quantity demanded↓) 2.) Income effect - A price increase reduces the consumer's purchasing power. A reduction in purchasing power will decrease the amount of normal goods bought, but increase the quantity of inferior goods bought. The change in quantity purchased due to a change in purchasing power is called the income effect. -With the income effect whether the quantity demanded ↑ or ↓ is dependent on if it's a normal or inferior good. (Price↑, demand for inferior good↑, this goes in the same direction as the substitution effect), & (Price↑, demand for normal good↓, this works against the substitution effect). The total effect of the price increases is the sum of the substitution and income effects. -In the 1st image, the consumer has an income of $120, and the initial price of shelter is $6 (budget constraint B0) but rises to $24 (budget constraint B1). The optimal bundle shifts from A to D, this movement is called the total effect of the price increase. The indifference curves are represented by the I's. -In the 2nd image, we ask how much income would the consumer need to reach his original indifference curve (I0, i zero) after the increase in the price of shelter? (A=$240). Remember, shelter is a NORMAL GOOD. If the consumer's income increased by $240 it would undo the loss of purchasing power from the increase in the price of shelter. However, because of the substitution effect of the price change, it would shift the optimal bundle along the indifference curve, from A to C. Also notice here that consumption of shelter has decreased, this is because the price of shelter has increased. A movement from C to D would be a result of the income effect. -In the 3rd image, the substitution effect pushes us from point A to C, which reduces demand for hamburgers from 12 to 8. Remember hamburgers are an INFERIOR GOOD. Recall that with inferior goods, the income effect increases demand for inferior goods; thus, when the income effect kicks in we shift from point C to D, where demand for hamburgers increases from 8 to 9. This is the opposite of the 2nd image. -NOTE: The image is called "3 income effect graphs"
A decrease in demand -->
A decrease in demand --> a decrease in both the equilibrium price and quantity
A decrease in supply -->
A decrease in supply --> an increase in the equilibrium price and a decrease in the equilibrium quantity
Consumer Surplus
A dollar measure of the extent to which people benefit from a transaction. This dollar measure is called consumer surplus.
Indifference map
A graphical representation of the entire set of a consumer's indifference curves. Bundles on higher indifference curves are more preferred than bundles on lower indifference curves.
Price support / Price floor
A minimum price for a good, supported by the government's offer to buy the good at that price. It creates an artificially high price, which increases the supply, creating a surplus that the government has to buy. - Purpose of farm price supports is to ensure prices are high enough to provide adequate income for farm families. However, the excess bought by the government often goes to waste; thus, a price floor above equilibrium is bad. - In the picture; the equilibrium in this soybean market should be P=$300/ton and Q=300,000 tons/yr. The gov creates a price support (price floor) of $400/ton to raise the income of farmers. The quantity supplied increases to 400,000 tons/yr while the quantity demanded falls to 200,000, causing excess supply 200,000 for the government to buy.
Preference Ordering
A ranking of all possible bundles in order of preference. Everyone has different rankings, but there are 4 simple properties of preference ordering 1.) Completeness - The consumer must be able to rank all possible combinations of goods. Ex: If they were unfamiliar with a product and had no preference it wouldn't work 2.) More is better - other things equal, more of a good is preferred over less. Ex: If the price for 6 hotdogs was the same as for 4, you would buy the 6 3.) Transitivity - For any 3 bundles, A, B, and C, if A is preferred over B, and B is preferred over C, then A must be preferred over C. 4.) Convexity - Mixtures of goods are preferable to extremes. Ex: Small apartment and good food is better than massive apartment and no food. So, moderate amounts of goods are better than extreme amounts
Indifference Curve
A set of bundles among which the consumer is indifferent. So, consumers are indifferent to any bundle along this curve (A is equal to B, B equal to C, and so on). However, any bundle above the indifference curve (L) is preferred. And any bundle under it (K) is NOT preferable. -Only 1 indifference curve is shown in this graph. Realistically there would be a separate indifference curve for L and another one for K with more bundles along those. (ubiquitous) 4 properties of indifference curves 1.) Indifference curves are ubiquitous (found everywhere). So, any bundle has an indifference curve passing through it. Comes from the "completeness" property 2.) Indifference curves are downward sloping. This comes from the "more is better" property 3.) Indifference curves can NEVER cross. 4.) Indifference curves become less steep as we move downward and right. This comes from the "convexity" property.
Utility Function Ex: If there is 4 food and 3 shelter, what is the utility function?
A way other than an indifference curve to represent a consumer's preferences. Each bundle has a different utility function number; calculated with this formula, U = FS where, F = food; S = shelter; U = satisfaction of food and shelter -The preferred bundle will be the one with the highest utility function #. The utility number is called a util -Each point on an indifference curve will yield the same utility function, the same # of utils. Thus, utility along an indifference curve remains constant 4x3 = 12 utils
Trade offs between goods
An important part of a consumer's preference is the rate at which they are willing to exchange, or "trade off," one good for another. This rate is represented at any point on an indifference curve by the marginal rate of substitution (MRS), which is the value of the slope of the indifference curve at that point. So, there is a different MRS at each bundle on the curve. -Its the amount of food the consumer must be given to compensate for the loss of 1 unit of shelter (or vice versa). -Because of convexity, MRS declines as we move downward to the right along the indifference curve MRS = |ΔF| x |ΔS| (Dont understand how to calculate???)
An increase in demand -->
An increase in demand --> an increase in both the equilibrium price and quantity
An increase in supply -->
An increase in supply --> a decrease in the equilibrium price and an increase in the equilibrium quantity
The Unit Free Property of Elasticity
Another way of measuring responsiveness to changes in price is to use the slope of the demand curve. -Quantity demanded of a good with a steep demand curve will be less responsive to changes in price -When weighing cost and benefits, always compare absolute dollar amounts, not proportions. But when describing how quantity demanded responds to changes in price, it's generally best to speak in terms of proportions.
Chapter 5
Applications of rational choice and demand theories Chapter outline -Using the rational choice model to answer policy questions -Consumer surplus -Overall welfare comparisons -Using price elasticity of demand -Intertemporal choice model
How does changes in income affect normal and inferior goods?
As a consumers income rises, the quantity of normal goods a consumer will buy INCREASE As a consumers income rises, the quantity of inferior goods a consumer buys will REDUCE. In the image, both (a) and (b) show an Engel curve. (a) - The quantity demanded increases with income as this is a normal good (b) - The quantity demanded decreases with income as this is an inferior good
[ALGEBRA] The supply schedule is: P = 2 + 3Qs; The demand schedule is: P = 10 - Qd. Find the equilibrium price
At equilibrium we know that Qs = Qd; or, supply equals demand. Thus, 2 + 3Q = 10 - Q 3Q + Q = 10 - 2 4Q = 8 Q = 2 So, to find the equilibrium price (P) we use the given demand schedule. P = 2 +3 Q; or, P = 2 + (3) (2) which is: 8
Budget Constraint
Budget constraint / Budget line - The set of all bundles that exactly exhaust the consumer's income at given prices. -Its slope is the negative of the price ratio of the two goods. So, the slope of the budget constraint is -Ps/Pf -The budget constraint is a straight line; any point along the line is attainable and represents the max amount of goods A & B that can be purchased. PsS + PfF = M -This is necessary for the budget constraint because it means that all expenditures equal the income available. or, F = (M/Pf) - (Ps/Pf)S -This gives the food endpoint Maximum food = M/Pf Maximum shelter = M/Ps Where, M = income F = quantity of food S = quantity of shelter Pf = price of food Ps = price of shelter
Suppose butter and toast are perfect complements, using one pat of butter for each slice of toast. Butter costs $0.20, toast $0.10, and the consumer has $12 to spend. How much toast and butter will be consumed.
Budget constraint: PbB + PtT = M 0.2B + 0.1T = 12 Max butter: M/Pb; 12/0.2 = 60 Max toast: M/Pt; 12/0.1 = 120 Slope = -Pb/Pt; 0.2/0.1 = -2 These two are preferred equally, so, B=T. Thus, we replace B with T (or vice versa) and solve for T. 0.2B + 0.1T = 12 0.2T + 0.1T = 12 0.3T = 12 T = 40 -So, 40 slices of bread & butter are consumed.
Nonlinear budget constraints (kinked)
Budget constraints are typically linear due to prices being constant, but budget constraints can be nonlinear when prices vary with quantity, such as with quantity discounts.
Opportunity Set (Bundle)
Bundle - A particular combination of two or more goods, such as shelter and food. Ex: Bundle A might be 4 food and 8 shelter, whereas bundle B might be 6 food and 6 shelter
Affordable set (feasible set)
Bundles on or below the budget constraint (budget line). These are the bundles for which the expenditure at given prices is less than or equal to the income available. Ex: Bundle D and bundles on the line. Here, F=4, and PF=10; thus that's $40 in food. S=5, PS=5, so that's $25 on shelter. Overall, that's $65, which is less than the income of $100
Unaffordable set (unfeasible set)
Bundles that are outside of the budget constraint (budget line) Ex: Bundle E. F=8 for $80, and S=12 for $60. This is over $100 and thus unattainable
Change in Demand versus Change in Quantity Demanded
Change in demand: a shift in the entire demand curve forward or backward -ex: when the average income level of buyers changes, the demand curve shifts Change in quantity demanded: a movement along the demand curve. Changing point along the demand curve. -ex: when the price of a good falls, the result is an increase in the quantity demanded, not an increase in demand So, a change in price creates a movement ALONG the demand curve, whereas a change in income level SHIFTS the demand curve
Rationing function of price
Changes in prices distribute scarce goods to those consumers who value them most highly. Ex: If the price of a product rises, those who value it the most will continue to buy it.
Application: A bias in the consumer price index
Consumer price index (CPI) measures changes in the "cost of living," which is the amount a consumer must spend to maintain a given standard of living -However, the CPI fails to take substitution into account hence overestimating the cost of living. So, when the price of a good rises the CPI says the cost of living has increased, whereas in reality the consumer will simply substitute for a cheaper alternative. -The extent to which CPI overstates the cost of living will go up as substitution possibilities increase. The bias will also be larger when there are greater differences in the rates of increase of different prices.
Using indifference curves to describe preferences
Different consumers have different SLOPES of their indifference curves (different MRS at points). Ex: in the picture Tex is willing to exchange 1 lb of potatoes for 1 lb of rice at bundle A; but for bundle A Mohan is willing to trade 2 lb of potatoes for 1 lb of rice - they value goods differently, and so they have different different indifference curves.
You have current income of $100,000 and future income of $154,000, and can borrow and lend at the rate r=0.1 under these conditions you consume exactly your income in each period. True or false; an increase in r to r=0.4 will cause you save some of your current income
Given r=0.1 -The horizontal intercept is the present value of lifetime income, which is PV=M1+(M2/(1+r)); or, 100,000+(154,000/(1+0.1)) = 240,000 -The vertical intercept when r=0.1, we have: M1(1+r) + M2; thus, (100,000)(1+0.1) + 154,000 = $264,000 Given R=0.4 -New horizontal intercept: PV=M1+(M2/(1+r)); or, 100,000 + (154000/(1+0.4)) = 210,000 -New vertical intercept: M2+(M1)(1+r); or, 154000 + (100,000)(1+0.4) = 294,000 MRTP = |ΔC2 / ΔC1|, or, (264000-294000) / (240000-210000) = -1; thus, the answer is false because he wants more future income. He will consume less now and more in the future. We shift from point A to point D -NOTE THIS ABOVE IS NOT FROM BOOK??? It says "the optimal budget occurs at A, by assumption, which implies that the MRTP at A is 1.1"
Giffen Goods
Goods that are consumed more as the price of the good rises because it is a very inferior good whose income effect overwhelms its substitution effect when price changes. -This good makes up a large part of an individual consumer's budget so when the price for it rises, the consumer's purchasing power falls. And this good is so inferior that when the consumer's purchasing power falls they buy more of it, even though it's price has increased - so, it has no substitutes. -tldr; inferior good who's quantity demanded rises as its price rises
Income elasticity of demand
If a good exhibits a stable Engle curve, we can define its income elasticity of demand, the percentage change in the quantity of a good demanded that results from a 1 percent change in income. This measures the responsiveness of purchases to changes in the average market income. We use this formula to find income elasticity of demand, η = (Y/Q) x (ΔQ/ΔY) Where, η = Income elasticity of demand Y = average market income -Goods with an income elasticity less than 1 are necessities and a change in income has a minimal effect on the quantity demanded at any price. Ex: Food -Inferior goods will have η less than 0 -Luxuries have an income elasticity greater than 1. Ex: jewelry.
Welfare of people in respect to equilibrium price/quantity
If price and quantity take anything other than their equilibrium values, some people can be made better off without harming others. Ex: If P=$8 but quantity supplied is only 2,000, and people are willing to pay up to $16 (demand) everyone wins. Those selling lobsters get to sell their product for more and people are willing to pay more to get the lobsters so the lobster sellers win and the customers aren't harmed (even though they're paying too much)
If a consumer is confronted with exactly the same budget constraint in two different situations, they should make the same decision, right?
If they were rational, yes. However, in reality this is not the case. The situation in which the budget constraints are presented often influence the consumers decision. -Ex: If you lose $5 on the way to Starbucks you will probably end up buying the drink anyways. But, if you buy the drink and then spill it, you are less likely to buy another. Either way the cost would be the same (same budget constraint) but you're decision will probably be different.
Corner Solution
In a choice between two goods, a corner solution is a case in which the consumer chooses only one good. Ex: The far ends on a budget constraint, where the consumer chooses max food and no shelter -This usually only happens when goods are close substitutes, rather than essentials like food and shelter
Cardinal vs Ordinal Utility
In previous examples we assumed people were able to rank each possible bundle in order of preference, this is called the ordinal utility approach. They were ranking them like A is better than B; but, they were not quantitatively ranking them. Ex: They couldn't rank them like "A is 6.43 times better than B." Assuming people could rank goods in such a way (A is 6.43 times better than B) is called the cardinal utility approach. It assumes that the satisfaction provided by any bundle can be assigned a numerical, or cardinal, value by a utility function. U = U(X,Y) where X&Y are 2 goods. -The cardinal utility function is graphed. It's like a mountain, with NO summit. But, we can cutaway the mountain to create indifference curves. -Crazy math, calculus and such that I skipped over.
Determinants of Demand
Incomes -Normal goods: the quantity demanded at any price rises with income -Inferior goods: the quantity demanded at any price falls when income rises. Ex: Ramen noodles Tastes If something becomes more popular the demand for it will increase Price of Substitutes and Complements -Complements: an increase in the price of one good decreases demand for the other good; and vice versa. Ex: butter & toast. -Substitutes: an increase in the price of one will tend to increase the demand for the other. Ex: coke & pepsi Expectations Population The more people there are the greater demand is.
Aggregating Individual Demand Curves
Individual demand curves are combined to form the market demand curve. Ex: Given a market for shelter, with only 2 consumers. To create the market demand curve, we pick a price (say, $4) and add the quantities demanded by each consumer at that price. We repeat this process with other prices (say, $8). Note that at $8 only 1 of the 2 consumers is willing to buy shelter at all, so we have only 1 point. -We combine all the points that are given at different prices to get the market demand curve.
What happens if both price doubles? So, the price of shelter doubles from $5 to $10, and the price of food also doubles from $10 to $20. Income is still $100
It has the same effect on the budget constraint as if income fell in half. PsS + PfF = M 10S + 20F = 100 Slope: -Ps/Pf -10/20 = -0.5 Maximum food = M/Pf 100 / 20 = 5 Maximum shelter = M/Ps 100 / 10 = 10 When the price of both doubles, the max food and max shelter is cut in half. However, the slope is unchanged.
Real price of a product
Its price relative to the prices of other goods and services Ex: If inflation rises the real price of the good stays the same, regardless of the fact you're paying more.
A gas tax and rebate policy (Jimmy Carter raising gas taxes example)
Jimmy Carter imposed new gas taxes in order to reduce gas consumption to make the US less dependent on foreign oil. Obviously this would hurt the poor, so Carter proposed using the proceeds of the gas tax to reduce the payroll tax, meaning their paychecks would be larger. So, they would get their tax money back as if there was no tax, and critics said they would just use that money to buy more gas, However this is wrong because of rational choice.
Econ 323 Chapter 3
Learning objectives 1.) Describe the consumer's budget constraint, the set of all combinations of goods that can be purchased with given income and prices 2.) Show how the budget constraint changes when income and prices change 3.) Describe the consumer's preference using an indifference map 4.) Show how the consumer's budget constraint and indifference map interact to determine the combination of goods to purchase
Application for Price Elasticity of Demand In 1987 the Metropolitan Atlanta Rapid Transit Authority (MARTA) raised its basic fare from 60 to 75 cents/ride. In the following 2 months revenue rose 18.3% in comparison with the same period a year earlier. What do these figures tell us about the original price elasticity of demand for rides on the MARTA system?
Math is hard and I don't understand it. Anyways, Because the fare increase led to a substantial increase in total expenditure, demand is highly inelastic.
James views car washes and gas as perfect complements in a 1 to 10 ratio, requiring 1 car wash for every 10 gallons of gas. Gas costs $3/gal and James has $144 to spend. Construct Jame's demand curve for car washes by considering his quantity demanded of car washes at various prices (such as $6, $18, and $42).
Max gas: 144/3 = 48 Max carwash at $6: 144/6=24 Max carwash at $18: 144/18=8 Max carwash at $42: 144/42=3.4 -SO, We graph these values and then find the optimal bundle like so, At carwash $6 3g + 6w = 144 3(1g) + 6(0.10g) = 144 g = 40 40x3=120, 120-144=24, 24/6=4w SO, at $6 for carwash we will buy 40gas and 4carwash -We repeat this process for each price and graph it to show the demand changes for a price increase in carwashes. Using the above points we can create Jame's demand curve for carwashes at various prices.
Example for above card and picture (Using demand curves to measure consumer surplus): Suppose the demand for shelter is P = 15 - Q. What is consumer surplus at P = $3?
P = 15 - Q -P is our max price. Then plug in our price ($3) for P and solve for Q P = 15 - Q, or, 3=15-Q, thus, Q=12. -Our quantity demanded is 12
A tennis club rents courts at $25 per person per hour. John's demand curve is given by P = 50 - (1Q/4), where Q is measured in hours. Assuming there are no other tennis clubs in town, what is the max annual membership fee John would be willing to pay for the right to buy a court at $25/hr? (b) How much would the maximum annual membership fee be if the club charged only $20/hr for court time?
P = 50 - (1Q/4 25 = 50 - (1/4)Q P=50(4/1) - (1Q/4)(4/1) (4/1)P = 200 - Q Q = 200 - (4/1)P or, Q = 200 - (4)(25) Q = 100 Thus, Q = 100. So, at $25 the quantity demanded is 100 Our max point is $50 in price (from P = 50 - (1Q/4) and our max quantity is 200 (from Q = 200 - (4/1)P) John would be willing to pay up to the entirety of his consumer surplus. This amount is equal to the area of the triangle (the consumer surplus). Area of a triangle = (1/2) (base x height) (1/2) (100 x 25) = $1,250 (b) Our maxes would remain the same; however, at $20 our quantity demanded changes to: Q = 200 - (4)P, or, Q = 200 - (4)(20); thus, Q=120 And, our consumer surplus changes to: (1/2) (120 x 30) = $1,800 -Note, our 30 comes from the height, which is the distance from our current price to the max height; thus, 20 - 50 = 30
Suppose a market has 10 consumers, each with demand curve P=10-5Qi where P is the price and Qi is the number of units demanded by the ith consumer. Find the market demand curve
P=10-5Qi Qi=2-(1P/5) -Then we multiply by the number of consumers, Qi=2(10)-(1P/5)(10) Qi=20-2P -Thus, we end up with both of our points. But, then we rearrange the market demand curve to have price alone on one side, returning to the slope intercept form. Q=20-2P, becomes P=10-(1Q/2) In general, for a market with identical individual demand (P=a-bQi) the market demand will be P=a-(b/n)Q
Explain the parts of this equation. PB = PS + T
PB is the price the buyer pays. It consists of the amount the seller earns (PS) and the tax paid (T). Keep in mind the seller only gets PS
Application: The Permanent Income and Life Cycle Hypothesis
Permanent income hypothesis says that the primary determinant of current consumption is not current income but what he called permanent income. -Permanent income is the present value of lifetime income -Consequently, a large increase in current income will yield only a small increase in permanent income, so the effect on current consumption would be less than an equivalent increase in permanent income.
Price ceiling (ex: Rent controls)
Price ceiling - The limit to which the price of a good can rise. By law, it cannot go above this point. Ex: Rent controls - Rent controls increase quantity demanded (by capping the price sometimes below equilibrium), and decrease quantity supplied, which causes excess demand. In the picture; limiting rent to $400/mo (rather than the market rate of $600) creates an excess demand of 40,000 units. 80,000 units are demanded but only 40,000 supplied.
The effect of changes in price (Price Consumption Curve, PCC)
Price consumption curve (PCC) - for a good X is the set of optimal bundles traced on an indifference map as the price of X varies (holding income and the price of Y constant). Recall from CH2 that a market demand curve tells how much of a good the market wants to buy at various prices. We want to make a demand schedule for a good, ex shelter, for a single consumer (not the entire market) to see how a change in price of shelter effects how much the consumer buys. So we make an indifference map, plot shelter on the horizontal axis and the composite good Y on the vertical axis. If we have the consumers income (say, $120) and the price of the composite good (say, $1) we could find the best affordable bundle at different prices for shelter. So, there would be a best affordable bundle at $24, and a different one at $12, and 6$, and $4. If we were to draw a line through each of these best affordable bundle points we would get our Price Consumption Curve (PCC). In the image, Y = Consumers income ($120) PCC = Price consumption curve -Each dot is a best affordable bundle at a certain price for shelter -Here, income and the price of Y are fixed, and we change only the price of shelter. Notice that each time the price of shelter falls, the consumer is willing to buy more shelter. Also notice that the amount spent on the composite good falls when the price of shelter drops from $24 to $12 but rises when the price of shelter drops from $6 to 4$. This is a common pattern.
Price Elasticity of Demand
Price elasticity of demand is defined as the percentage change in the quantity of a good demanded that results from a 1 percent change in price. This value will always be negative, or zero Ex: If a 1% change in the price of shelter caused a 2% reduction in the quantity of shelter demanded, then the price elasticity of demand for shelter would be -2, making it elastic -The demand for a good is elastic with respect to price if its elasticity is less than -1 -The demand for a good is inelastic with respect to price if its price elasticity is greater than -1, and unit elastic if it's price elasticity is equal to -1
The Engel Curve
Similar to the individual demand curve, the Engel Curve takes the quantities of shelter demanded from the ICC and plots them against the corresponding values of income. The Engel Curve tells us how much shelter the consumer will buy at various levels of income. -Notice that on Y axis of the ICC we graph the amount the consumer spends on all goods other than shelter (composite goods), but on the vertical axis of the Engel curve we measure the consumer's income.
Nonlinear budget constraint example: A power company charges $0.10 kilowatt-hour (kWh) for the first 1,000 kWh of power purchased by a residential customer each month, but only $0.05/kWh for all additional kWh. For a residential customer with a monthly income of $400, graph the budget constraint for electric power and the composite good - don't have to graph, just find the slope for the first 1,000kWh and the cost; then find the slope for the additional kWh (the composite good, since it's what left over income is spent on) and how much more kWh can be bought
Slope = -Px. -0.10 for the first 1000kWh, which will cost (1000 x 0.10) = $100. Remaining income, $400 - $100 = $300 Slope = -0.05 300 / 0.05 = 6,000kWh -Thus, the remaining $300 can buy 6000kWh more with a slope of -0.05
Given a consumer's income is M=$100, all of which is spent on food and shelter. Food costs are $10 and shelter costs are $5. -Find the slope -Find the equation for the budget constraint -Find the maximum amount of food and shelter that can be purchased
Slope: -Ps/Pf -5/10 = -0.5 The slope indicates that the opportunity cost of an additional shelter is 1/2 food PsS + PfF = M 10S + 5F = 100 Maximum food = M/Pf 100/10 = 10 Maximum shelter = M/Ps 100/5 = 20 Note: at the max for one good we are buying none of the other good. These points are represented as L & K on the budget constraint line
Soybeans are an input for beef production. What happens if soybeans become more expensive?
Soybeans becoming more expensive causes a reduction in supply of beef, causing the price of beef to increase and quantity to decrease.
Determinants of Price Elasticity of Demand -Substitution possibilities -Budget share -Direction of income effect -Time
Substitution possibilities - The substitution effect of a price change tends to be small for goods with no close substitutes -Ex: Antidote for snake bite. If you get bit you have no substitute, so demand is highly inelastic. Salt. Budget share - The larger the share of total expenditures accounted for by the product, the more important will be the income effect of a price change. -Ex: Salt accounts for a small share of total expenditure, so the income effects of a price change are negligible. However, for goods like housing, the income effect of a price change is likely to be large because you spend a large part of your income on it. -The greater the total expenditure accounted for by the good, the more elastic demand will be. -So, the budget share tells us whether the income effect of a price change is likely to be large or small Direction of income effect - The direction of the income effect tells us whether the income effect will offset or reinforce the substitution effect. A normal good will have a higher price elasticity than an inferior good, because the income effect reinforces the substitution effect for normal goods but offsets it for an inferior good Time - Demand for a good will be more responsive to price in the long run than in the short run. -Ex: If gas prices rise you can't really drive less; however, in the long run you can buy a more efficient vehicle. -The long run demand curve is more elastic than the short run demand curve
Excess demand
The amount by which quantity demanded exceeds quantity supplied. Shortage
Excess supply
The amount by which quantity supplied exceeds quantity demanded. Surplus
What happens if the price of both goods change by the same proportion?
The budget constraint shifts parallel to the original one
What happens if income decreases? -Ex: Suppose income is cut in half from M=$100 to $50, while the prices of food and shelter remain the same. Find the new budget constraint, slope, maximum shelter, and maximum food.
The budget constraint shifts parallel to the original one. PsS + PfF = M 5S + 10F = $50 or, F = 5 - (1/2)S Slope: -Ps/Pf -5/10 = 0.5 Slope remains unchanged. Although the entire budget constraint line shifts Maximum food = M/Pf 50 / 10 = 5 Maximum shelter = M/Ps 50 / 5 = 10 The max for both food and shelter is cut in half.
How does a tax increase affect the buyer and seller?
The buyer's share of the tax burden is how much the price paid by the buyer increases because of the tax (the price rises as a result of the tax because they buyer now has to pay for the product AND the tax) tB = (PB - P*) / T where P* = equilibrium price, and T = tax, tB = tax burden paid by the buyer. This equation gives the percent of the tax burden paid by the buyer A tax can be levied on either the seller or buyer; if it's on the seller it costs them more to produce, so the suppliers/sellers end up paying the tax - this shifts the supply curve (reducing supply). However, over time the price will be raised to account for the increased production cost which will force the buyer to also pay the tax, so it adjusts towards a new equilibrium. But, at first the tax can be paid by either the seller or buyer, depending on who it's put on - but the overall burden will be felt by everyone. "Tax on the buyer leads to the same outcome as a tax on the seller." ------------------------------------------------ The seller's share of the tax burden is how much the price received by the seller decreases because of the size of the tax tS = [(P* - PS) / T] tS = portion of tax paid by the seller. The tB + tS would be the total tax paid by both the seller & buyer tB + tS = 100%
Intertemporal choice model
The choices we've considered thus far have all taken place in the present, ex: food vs shelter now. The intertemporal choice model looks at how rational consumers distribute their consumption over time. There are 2 assumptions; 1.) There are only 2 periods, current and future 2.) Alternatives will be current consumption (C1) or future consumption (C2). Each of these is an amalgam, the equivalent of the composite good In the image, bundle E is current consumption of $6,000 combined with future consumption of $6,000; whereas bundle D is current consumption of $3,000 and future consumption of $9,000.
Best feasible bundle / Best affordable bundle Example: Ps=$5, Pf=$10, at income=$100. What is the
The consumer combines the indifference map, which says which bundles are more preferable, with the budget constraint, which says which bundles are affordable, to find the best affordable bundle. In the graph, G is the most preferred because it lies on the highest indifference curve. However, G is outside of the budget constraint so it's not affordable. F is the best affordable budget -The best bundle will always lie at the point of tangency and the MRS will always be the same as the slope Slope: -Ps/Pf -5/10 = -0.5 Thus, the opportunity cost of an additional shelter is 1/2 food. For problems like this, the MRS is the same as the absolute value of the slope. Thus, MRS=PS/PF. Which is 0.5
SNAP (Food stamp program) vs. Cash grant Ex: Consumer has income of $400, food stamp vs cash grant of $100
The goal is to reduce hunger. People whose income is below a certain level receive food stamps to purchase only food items. The government gives food retailers cash for the stamps they collect. So, if someone is given $100 in food stamps and spends it all on food; would they have been better off being given $100 directly in cash? To determine the answer we must find out which alternative creates a higher indifference curve. -With the $400 income and $100 in food stamps, he can buy a max of $500 food; this is exactly the same as with the cash grant. But, lets say he has 2 things he spends money on, food, and everything else (the composite good). So, the difference then is how much he can spend on the composite good. His max composite good with food stamps is $400, vs $500 with the cash grant. -If the consumer was planning on spending $100 on food regardless, the consumer buys the same bundle regardless -Overall, the cash grant puts the consumer at a higher indifference curve. Ex: If the consumer is spending less than $100 on food they would have some left over with the cash grant.
2 important polar cases
The horizontal demand curve, with a slope of zero, has an infinitely high price elasticity at every point. Demand curves like this are called perfectly elastic The vertical demand curve has a price elasticity everywhere equal to zero, it's called perfectly inelastic -Ex: Salt. It's cheap and used consistently and it would take a massive increase in price to change your consumption of it, so it's practically perfectly inelastic.
Cross Price Elasticity of Demand
The percentage change in the quantity of one good demanded that results from a 1 percent change in the price of the other good. The cross price elasticity of demand is found using this formula, ЄXZ = (ΔQx/Qx) / (ΔPz/Pz) Where, X&Z represent products Qx = quantity of X Pz = price of Z ЄXZ = measures how the quantity demanded of X responds to a change in the price of Z -The cross price elasticity may be either positive or negative. -X&Y are complements if ЄXZ is less than 0, but substitutes if ЄXZ is greater than 0 -Ex: A rise in the price of coffee will increase the demand for tea
Equilibrium quantity and price
The price-quantity pair at which both buyers and sellers are satisfied. It's the price at which quantity supplied equals quantity demanded. Shown is an equilibrium graph. Here, equilibrium is Q=3000, P=$12
Allocative function of price
The process whereby price acts as a signal that guides resources away from the production of goods whose prices lie below cost toward the production of goods whose prices exceed cost. Ex: If there is a surplus of jeeps but a shortage of trucks (due to price changes), resources are diverted away from producing jeeps and toward producing trucks.
The Dependence of Market Demand on Income Ex: Two consumers A & B are in the market for food. Their tastes are identical and each has the same initial income level, $120. How will the market demand curve for food be affected if A's income goes down by %50 while B's goes up by %50? (just look and analyze image)
The quantity of a good demanded any person depends not only on its price but also on the person's income -Since the market demand curve is the horizontal sum of individual curves, it too will be influenced by consumer incomes -Notice in the image that the food consumed increased by only a little bit with an increase in income, this is because you can only eat so much so at a certain point it wouldn't increase at all. So, the market demand here depends on the distribution of income, where adding more money to the rich has little effect on demand.
What happens if the price of one good goes up but the price of the remains the same? -Ex: Suppose the price of shelter doubles from Ps=$5 to $10, while income and the price of food remain the same. Find the new budget constraint, and maximum shelter
The slope and budget constraint shifts because the max is now less for the good who's price has increased; however, the max (endpoint) for the other good remains the same. 10S + 10F = 100 Maximum shelter = M/Ps 100/10 = 10 Thus, maximum shelter is cut in half and the budget constraint is more steeply downward sloping.
Application: School vouchers -What is the effect of vouchers on the level of resources devoted to education?
There is a policy proposal that in order to improve education through competition each family should be given a voucher that could be used toward the tuition at any school of the family's choosing. -Currently, families who choose to go to private schools do not receive a refund on their school taxes We can use the rational choice model to examine the educational choice families face. Suppose in taxes each family pays Pe for 1 unit of public education, where 1 unit is defined as a year's education. If the family chooses to, they can send their kid to private school and buy 1 unit of education also at price Pe per unit. -A families pretax income is Y, lets make a budget constraint. If there were no taxes or school expenses the families budget constraint would be line ABD. But, since each family must pay Pe school taxes, the budget constraint is Y - Pe. This drops us to A' because they're required to pay so their income drops, but since the 1st unit of education is free, there is a straight line from A' to B. Thus, our budget constraint is A'BCE, with an optimal budget of B. -The second image shows the new budget constraint, A'BD, with a school voucher. Here, G is the optimal bundle
The Individual Consumer's Demand Curve
This is like the market demand curve because it tells us the quantities the consumer will buy at diff prices. The information for the individual demand curve comes from the PCC. So, we record the quantities of shelter that correspond to the shelter prices on each budget constraint from the PCC. Then, we graph these values with price on the Y axis and quantity of shelter demanded on the x axis. -Recall from CH3 that the price of shelter along any budget constraint is given by income divided by the horizontal intercept of that budget constraint.
Intertemporal indifference curves
This tells us a consumers preference over current and future consumption. In the image, the consumer is indifferent between the bundles on I1, but they're less desirable than the bundles on I2, and so on. -The absolute value of the slope of an indifference curve at a point is called the marginal rate of time preference (MRTP) at that point. The MRTP at A is: | ΔC2 / ΔC1 |. Where it's initial - final. This is the marginal rate of substitution between future and current consumption. -If MRTP is greater than 1, the consumer exhibits positive time preference at that point - this means that he requires more than 1 unit of future consumption to compensate him for the loss of a unit of current consumption. -If MRTP is less than 1 then he exhibits negative time preference at that point. Here, he is willing to forgo 1 unit of current consumption in return for less than 1 unit of future consumption. -MRTP declines as you move downward along an indifference curve, because the more current consumption someone has the more they're willing to give up in order to obtain an additional unit of future consumption -Finally, if MRTP is = 1, the consumer has a neutral time preference. Here, present and future consumption trade off against each other at the ratio of 1 to 1 The image shows us the optimal allocation between current and future consumption.
Income Consumption Curve (ICC)
To create the PCC for shelter, we held preferences, income, and the price of the composite good constant, then looked at the effects of a change in the price of shelter. For ICC, we hold preferences, price of the composite good, and the price of shelter constant, and look at the effects of a change in income. Ex: We hold the price of the composite good constant at $1, the price of shelter constant at $10, and look at what happens when the income changes from, $40, $60, $100, and $120. -Recall from CH3 that a change in income shifts the budget constraint parallel. As income increases, the budget constraint moves outward. -There is a best affordable bundle at each income level. Drawing a line through these bundles produces the ICC. In this case it's a straight line but that isn't always the case
Application: Two Part Pricing
Two part pricing is a pricing scheme that consists of a fixed fee and a marginal charge for each unit purchased (also called two part tariffs) -The goal of this pricing strategy is to capture some of the consumer surplus, transferring it from the buyer to the seller
Using demand curves to measure consumer surplus
We can use the consumer's demand curve to measure consumer surplus. In both graphs, D represents an individuals demand curve for shelter, which sells for $3. In (a) the consumer would have been willing to pay $14 for shelter but the cost is only $3, so they obtain a surplus of $11 for the 1st unit, but the most he would pay for the 2nd unit is $14, so his surplus would be smaller for that unit ($10). And for the 3rd unit, a surplus of $9. Here, the height of the individual's demand curve at any quantity represents the most the consumer would pay for another unit.
Smith and Jones are the only consumers in the market for beech saplings. Their demand curves are given by P=30-2Qj and P=30-3Qs where Qj and Qs are the quantities demanded by Jones and Smith, respectively. What is the market demand curve for beech saplings in their town?
We solve the individual demand equations for the respective quantities in terms of price (vertically, NOT horizontally). Jones: P=30-2Qj, solve for Qj=15-P/2 Smith: P=30-3Qs, solve for Qs=10-P/3 -Here, the quantities demanded are represented by Q, so we have Q=Qj+Qs Thus, 15-(P/2) + 10-(P/3) 25-(5P/6)=Q -Solving for P we get the equation for the market demand curve, (5P/6)=25-Q (divide both sides by 5/6, but for Q that means multiplying by the denominator) P=30-(6Q/5) I'm confused on this, BUT, looking above we did get Q=25 and P=30, thus it makes sense with the graph. We can apply this same reasoning to the individual demand curves for Jones and Smith.
Composite good
We view the consumer's choice in goods as being between a particular good (X) and a combination of other goods (Y); this combination of other goods is called the composite good. We generally consider the composite good as the amount of income the consumer has left over after buying good X and, thus, the amount of income spent on goods other than X. -The price of the composite good is always 1 -Since we're grouping many goods into 1 category (Y) it's as if we only have 2 goods, X & Y. So, the budget constraint is a straight line. PxX + Y = M (all of the income is spent on regular goods and composite goods) or, Y = M - PxX (because whatever income is left over is spent on composite goods) M; Income Y; Quantity of composite good X; Quantity of good PxX; Price of X Py=1; Price of composite -Max composite is M. Since the price for composite goods is always 1. -Max good (X) is M/Px. We must divide since the price for X varies. -Slope = -Px.
Jin spends all his income on 2 goods, X & Y. His income is $750. -First year prices Px=10 and Py=20; he consumed X=50 and Y=25. -Second year prices Px=10 and Py=10; and income M = 750 -Which year is the individual better off?
We will compare Jin's budget constraints for the 2 years. For the 1st year PxX + PyY = 1,000, we will use this to build a budget constraint (and using the prices, quantities, and finding the max's) (I don't understand how they got their endpoints?) -Since he buys the same bundle this year as he did last he can't be worse off, since he can still afford it. And since the relative price of X increased, he will shift to consuming less X and be better off.
What happens when price is not at equilibrium?
When price is not at equilibrium, trading in the marketplace will be constrained. But, there will be an adjustment toward equilibrium resulting from the natural reactions of self interested people facing either a surplus or a shortage.
Law of Demand
When the price of a product falls, demand for that product increases (Shown is a demand curve)
Law of Supply
When the price of a product rises, the supply of that product rises. (Shown is a supply curve)
Elasticity and Total Expenditure
Whether total expenditure rises or falls depends on if the gains from raising the price exceeds the loss of sales. -A price reduction will increase total revenue if and only if the absolute value of the price elasticity of demand is greater than 1; so, only if it's more elastic (like -5 or something). -An increase in price will increase total revenue if and only if the absolute value of the price elasticity is less than 1 (so, -0.5 for example) Total expenditure (R) is given by price x quantity, R = PQ
Marginal Utility
With an indifference curve, the best attainable bundle on the budget constraint is at the highest indifference curve. The best bundle would be at the point of tangency between an indifference curve and the budget constraint. Here, the slope of the indifference curve, or MRS, is equal to the slope of the budget constraint. With utility function, the best best bundle is on the budget constraint that has the highest level of utility. But, to find the actual best bundle we must use marginal utility. This is the rate at which total utility changes as the quantities of food and shelter change. Here, MUF represents each # of additional utils we get each additional unit of food, and MUS represents the # of utils we get for each additional unit of shelter. Slope of indifference curve at any point: MUF / MUS The marginal utility generated by the last dollar spent on food must match the marginal utility from the last dollar spent on shelter. As shown by this formula; (MUF / PF) = (MUS / PS) (MUS)(ΔS) = (MUF)(ΔF)
Example for Jimmy Carter tax: Suppose the price of gas is $1.00/gal, suppose a tax $0.50/gal is imposed that results in a $0.50 increase in the price of gas. Suppose a consumer is then given a lump-sum payroll tax rebate (so the rebate amount does not vary with the amount of gas he consumes) equal to the amount of gas tax he pays. Will this policy effect the amount of gas he buys? -Analyze using a consumer income of $150, and assuming his new income is $168 after the lump-sum payroll tax rebate
Yes. Also note that the rebate is like income from any other source. So, we want to see how the consumer responds to changes in income - thus, we use an income consumption curve (ICC) as shown in the image. The effect of the rebate is to offset partially the income effect of the price increase. It does nothing to alter the substitution effect. Note: There's a lot more math and information on PP's and book but I can't figure out how they got some of their #'s.
Point slope method
a method of calculating price elasticity of demand ε = (P/Q) x (1/slope) where, P = current price of a good Q = quantity demanded at that^price In the image, -The slope for a linear line will be the same at every point -To find the slope, we use this formula: Slope = ΔP/ΔQ Slope = -2 (why?) ε = (P/Q) x (1/slope) ε = (12/2) x (1/-2) ε = -3
If supply is perfectly elastic, who pays the tax? What if demand is perfectly inelastic?
tb = 100% If either of these scenarios are true, the buyer will pay the entire tax.
If supply is perfectly inelastic and a tax is levied, who will pay it? What if demand is perfectly elastic?
ts = 100% The seller/supply will pay it If demand is perfectly elastic, the seller will still pay it. If either of these are true then the seller will pay it
Elasticity and total expenditure example: Suppose you are the administrator in charge of setting up tolls for Golden Gate Bridge. Suppose that the toll is $3/trip and 100,000 trips are taken. If the price elasticity of demand for trips is -2.0, what will happen to the number of trips taken if you raise the toll by 10%? (b) Suppose that instead the price elasticity was not -2.0, but rather -0.5. How would the # of trips and total expenditure be affected by the 10% increase?
ε = -2 Price changes to: (0.10 x 3) + 3 = 3.3 Trips changes to: (0.10 x 2) = 0.20; (0.20 x 100,000) = -20,000 reduction. Thus, our trips changes to: 80,000 80,000 trips at 3.3$ = $264,000 BUT, at our original price, $3x100,000 = $300,000 -Thus, raising the price by 10% reduces total expenditure Recall: Price elasticity of demand is defined as the percentage change in the quantity of a good demanded that results from a 1 percent change in price -So, we have a 10% change. So, we must multiply our elasticity by 0.10 (b) ⊛Price still changes to: $3.3 ⊛Trips change to: (0.5 x 0.10) = 0.05; (0.05 x 100,000) = 5,000; (5,000 - 100,000) = 95,000 trips ⊛Our total expenditure changes to: $3.3 x 95,000 = $313,500
