# Practice Midterm Exam Microeconomics: Professor Owen Zidar

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2 1. SHORT ANSWER (40 points) State whether the following statements are TRUE, FALSE, or UNCERTAIN. You can take the non-italicized portions as given. For each of these problems, you must explain your answer with words, math, and/or pictures. The quality of the explanation is a substantial part of the grade. (a) Jill receives a \$10,000 per year scholarship to go to college. Jack is offered no financial aid of any kind. College tuition is \$25,000 per year, and college lasts four years. If both Jack and Jill decide to go to college, Jack s marginal willingness to pay for college must be greater than Jill s marginal willingness to pay for college. FALSE/UNCERTAIN. If Jack and Jill both decide to go to college we know that Jill s willingness to pay is greater than \$10,000/year and that Jack s willingness to pay is greater than \$25,000/year. However, both students willingness to pay might be very high (say \$100,000/year). Either could be higher. Both might be gaining consumer surplus from attending college. (b) A decrease in the price of capital reduces employment. The effect on capital is ambiguous because the substitution and scale effects go in opposite directions Higher wages cause firms to substitute towards capital at any given level of output (thus increasing capital usage) But the higher wage also raises marginal cost of output (assuming labor is a normal factor of production) which will reduce the use of capital (assuming capital is a normal factor) So are cheaper robots reducing employment? UNCERTAIN. It depends on magnitude of substitution and scale effects. (c) If, at your current consumption levels, your marginal utility for baseball tickets is higher than your marginal utility for football tickets, then you should go to more baseball games and less football games. UNCERTAIN: Unless I know the price of football tickets and baseball tickets, I do not know whether I should be consuming more of either. Note that the bundle of tickets that I should consume is determined by the equation: MU baseball MU football = p baseball p football Saying that the left-hand side of this equation is greater than 1 does not imply that the equation is not satisfied. The ratio of the

3 prices could be greater than one and the equation could be satisfied. Thus, it is not clear that I should buy more baseball tickets just because my marginal utility for baseball tickets is higher than my marginal utility for football tickets. Consider, for example, if the question had asked whether you should consume more cars and less candy bars. It is clear that if you had the choice, you would rather have an extra car for free than an extra candy bar for free. Thus, your marginal utility for a car is greater than your marginal utility for a candy bar. But, you should not necessarily consume more cars and less candy bars. Why? Because cars are more expensive. If you got a car, you would actually have to give up thousands of candy bars. (d) A plot of data regarding the price and quantity sold of ski lift tickets in Wisconsin over the past five years is presented below. These observations demonstrate that skiing in Wisconsin is a Giffen good during the time period indicated. FALSE or UNCERTAIN. The plotted points represent the price and quantity of lift tickets that were actually sold. These two values are determined by both supply and demand. In fact, they are the point where the supply and demand curves cross in each year. The pattern shown by the points could easily be explained by an increase in demand for Wisconsin skiing over time. If the demand curve shifted outwards each year and the supply curve remained unchanged, the resulting equilibrium would trace out the supply curve. Of course, we know even less than that, because we do not know if either or both curves moved around over time.

4 2. Consumer Theory (30 points) Consider an economy with two goods: cigarettes (C) and alcohol (A). The typical consumer s preferences are summarized by the utility function: U(A, C) = 3A + 3AC + 4C where A is the number of alcoholic drinks consumed in a month and C is the number of packs of cigarettes consumed in a month. The typical consumer sets aside \$102 to spend on cigarettes Question and 2: alcohol. The price of cigarettes is \$2 per pack; the price of alcohol is \$3 per drink. a) (a) On a graph with alcoholic drinks on the x-axis and cigarettes on the y- axis, draw the budget constraint. What is the slope of the budget line? Cigarettes Slope = -3/2 Alcohol (b) On the same graph draw an indifference curve that goes through the point representing b) the optimal consumption bundle. Label the optimal bundle. Without doing any calculus, what is the Marginal Rate of Substitution between cigarettes Cigarettes MRS=Slope of BL=-3/2

5 Alcohol b) and alcoholic drinks at the optimal consumption bundle? Cigarettes MRS=Slope of BL=-3/2 Optimal Cons. Bundle Alcohol (c) Write out the equation MU (in terms A 3+ 3Cof C and A) for the Marginal Rate of Substitution between c) MRS cigarettes CA = and alcoholic = drinks? MUC 3A + 4 MRS = MU A = 3 + 3C MU C 3A + 4 (d) How many alcoholic drinks and how many packs of cigarettes will the typical consumer purchase in a typical month? Two conditions are met at the optimal bundle: MU A MU C = p A p C (1) 3 + 3C 3A + 4 = C = 9A C = 9A + 6 C = 3A 2 + 1

6 2( 3A 2 2C + 3A = 102 (2) + 1) + 3A = 102 6A = 100 A = ( 6 C = ) + 1 = 26 2 (e) A tax on alcohol raises the price to \$6. How many alcoholic drinks will the typical consumer purchase in a month now? Do the same with new prices: MU A MU C = p A p C (3) 3 + 3C 3A + 4 = 6 2 = C = 9A C = 9A + 9 C = 3A + 3 2C + 6A = 102 (4) 2(3A + 3) + 6A = A = 96 A = = 8 C = 3(8) + 3 = 27 (f) Based on your answers, give an estimate of the price elasticity of demand for alcoholic drinks. or ε D = A 1 A 0 (A 1 +A 0 )/2 = p A 1 pa 0 (p A 1 +pa 0 )/2 ε D = A 1 A 0 A 0 p A 1 pa 0 p A ( )/2 6 3 (6+3)/ = = 1.04 =.52 Note that neither is very accurate approximation for such a large price change (i.e., 100%).

7 3. Supply and Demand (30 points) Market supply and demand for gasoline are: Q = P Q = P where P is the price per gallon and Q is the quantity in gallons. (a) On a graph with price on the vertical axis and quantity on the horizontal axis, draw the supply and demand curves. Label points where each curve hits the vertical and horizontal axes. What are quantity and price in equilibrium? P = P 50P = 400 P = 8 (b) How much is total consumer surplus? Q = = = 340 Consumer surplus is the area under the demand curve above the price line. This area is a triangle. The price that makes quantity demanded zero is 25. This is where the demand curve intersects the vertical axis. The height of the triangle is therefore 25 8 = 17. The width of the triangle is 340. Consumer surplus = 0.5 * 17 * 340 = 0.5 * 5780 = (c) The government introduces a price ceiling of 5 dollars per gallon. gasoline is bought and sold? How much Quantity demanded = *5 = 400 Quantity supplied = *5 = 250 There will be 250 gallons bought and sold in the market. An additional 150 gallons are demanded at the market price, but not produced. (d) Is there a surplus or shortage? How great is that surplus, or shortage? There is therefore a shortage of 150 gallons. (e) What is consumer surplus now that the price ceiling is in effect? You may ignore income effects. Are consumers as a group made better or worse off by the price

8 ceiling? Why? Only consumers who are able to buy the good get consumer surplus from it. To find consumer surplus we have to add up the difference between willingness to pay and the price paid for the 250 gallons bought in the market. This is equal to the area of the triangle labeled A plus the area of the rectangle labeled B. To compute these areas, we need to know the height of the demand curve at the point where Q = 250, or what the marginal consumer would be willing to pay for one more unit of X when supply is restricted to = P 20P = 250 P = So, the area of the rectangle B is ( )*250 = 1875 And, the area of the triangle A is 0.5 * ( ) * 250 = So, consumer surplus is = \$ Consumer surplus is higher with the price ceiling than it was without. Why? Well, two things happened that are relevant to consumers. First, the price is lower, which increases consumer surplus

9 for those who are able to buy the good. Second, supply is restricted because many producers choose not to produce the good at the lower price. This reduction in supply makes it so that many consumers who would like to buy the good at the market price are not able to. Some of these consumers would have bought the good even at the higher unrestricted price. Killing these transactions that would have happened at the equilibrium price reduces consumer surplus. In this case consumer surplus increases because the first effect is larger than the second. (f) The surplus/shortage you uncovered in part (d) leads to a political backlash against the price ceiling. After repealing the price ceiling law, the government decides instead to subsidize the supply side of the market. As a result of this new policy, producers will receive S dollars for each unit of gasoline that they produce and sell. [Hint: This will lead to a shift down of the supply curve of S dollars.] The government wants the equilibrium price paid by consumers, net of the subsidy, to be 5 dollars. What should the government subsidy rate (S) be to make this happen? Is this amount more or less than \$3? Why? The supply function is Q = P. We can rewrite this as 30P = Q 100 P = Q/30 100/30 The supply curve with the subsidy is this shifted down by S, which is: P = Q/30 100/30 S Or, we can rewrite this as a function of Q: Q = 30P S Figure out the equilibrium as a function of S: So, to make P=5 in equilibrium: Set the subsidy to \$5 per gallon. 30P S = P 50P = S P = 8 (3/5)S 5 = 8 (3/5)S S = 5

10 Why is the subsidy so high relative to the amount we want to reduce the price? Well, to get the price to be \$5 in equilibrium, the marginal consumer has to be willing to pay \$5 and no more. So, we have to induce the supply side to produce enough so that everyone willing to pay at least \$5 is satisfied. How much we have to subsidize the supply side to do this depends on the elasticity of supply. The more elastic supply is, the less we have to subsidize the producers to increase supply this much. The more inelastic supply is, the more we have to subsidize.

11 Formula Sheet Elasticity Taxes Price Elasticity (of Supply or Demand) is % Q % P, calculated in two ways. Point Elasticity: ε = P Q dq dp Arc Elasticity: (Q 2 Q 1 )/( 1 2 Q Q 2) (P 2 P 1 )/( 1 2 P P 2) Let P D be the consumer s (demander s) price, and P S be the firm s (supplier s) price Tax of \$t per unit: P D = P S + t Sales tax of τ per dollar sold: P D = (1 + τ)p S Tax incidence: Consumer Theory Consumers pay a share ε S ε S + ε D, producers pay ε D ε S + ε D Consumer s Problem: max U(x, y) subject to p Xx + p Y y M x,y Marginal utility: MU X = du dx, MU Y = du dy Marginal Rate of Substitution: MRS = MU X MU Y Optimal Consumption: Firm Behavior MRS = p X p Y, or equivalently MU X p X Profit = Revenue Costs = P Q C(Q) = MU Y p Y For inverse demand curve P (Q), revenue is Rev(Q) = Q P (Q). Marginal Revenue: MR = d dq Rev(Q) = P (Q) + QP (Q) Marginal Costs: MC = d dq C(Q) Profit maximization condition: MR = MC Math Formulas Area of a rectangle: base height Area of a triangle: 1 2 base height Derivative of a polynomial: d dx (a xb ) = a b x b 1 for constants a and b

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