Write your name: Suggested Answers UNIVERSITY OF WASHINGTON Department of Economics Economics 200, Fall 2008 Instructor: Scott First Hour Examination ***Use Brief Answers (making the key points) & Label All Graphs Completely and Carefully*** 1. (4 points) Consumer Equilibrium. A consumer has $50 per week to spend as she wishes on two goods vanilla lattes and pastries. The prices of those goods, the quantities she now buys, and her evaluation of the utility provided by these quantities are as follows: P Units Bought Total Utility Marginal Utility A) vanilla lattes 5.00 8 650 22.5 B) cheese Danish 2.50 4 950 15 For maximum satisfaction, this consumer should: a. Buy less of A and more of B. b. Buy the same quantity of A and more of B. c. Buy more of A and less of B. d. Buy more of A and the same quantity of B. e. Do nothing, being already at the best possible position. To justify your answer, state the utility-maximizing condition for consumer equilibrium and briefly explain (you do NOT need to provide a graph). Since (5.00 x 8) + (2.50 x 4) = 40 + 10 = 50, this consumer is spending all her income. So answers (b) and (d) are not feasible. The utility-maximizing condition for consumer equilibrium is (MUx/MUy) = Px/Py. Here, treating lattes as x, MUx/MUy = 22.5/15, which is less than 2 (30/15 would give 2) while Px/Py = 5.00/2.50 = 2. The rate at which this consumer is willing to give up Danish for lattes (22.5/15) is less than the rate at which she must give up Danish for lattes (2). Equivalently, the rate at which this consumer is willing to give up lattes for Danish (15/22.5) is more than the rate at which she must give up lattes for Danish (1/2). Therefore, the correct answer is (a): She should buy fewer lattes and more Danish. You could also say that by buying one less latte she can afford two more Danish, and the net change in utility is 22.5 + 15 + 15 = 7.5 > 0.
Economics 200 2 Scott 2. (4 points) Elasticity of Supply. State whether the following statement is true, false, or uncertain and explain your answer: In the diagram below, the supply curve S 2 is more elastic than the supply curve S 1. That is, the elasticity of supply is greater for S2 than for S1. P S 1 S 2 False. Elasticity is 1 everywhere on both S1 and S2. See Problem Set 2 answers for explanation. Q 3. (4 points) Incidence of a Sales Tax. Assume that the demand for fish is perfectly elastic, and the supply curve is rising. The current equilibrium price is $8.00 per pound. If the government imposes a sales tax of $2 per pound (requiring that producers send the government $2 for each pound of fish sold) what will the new equilibrium price of fish be? How much of the tax will consumers bear? How much of the tax will producers bear? Illustrate your answer with an appropriate graph of supply and demand. The picture would have a horizontal line at a price of $8.00 as the demand, and a standard upward-sloping supply. The effect of the tax would be to shift supply upward by $2.00. The new equilibrium will be at a lower quantity of fish but the equilibrium price will still be $8.00. Fish sellers keep only $6.00 per pound, however, bearing the entire burden of the tax.
Economics 200 3 Scott 4. Agriculture Policy, Supply and Demand, Demand Elasticity, Pareto Efficiency. The diagram below shows the supply and demand for an agricultural commodity, say grain. Quantity is measured in thousands of bushels per week, price in $ per bushel. P S 9 5 2 D Q 3 7 10 a. (4 points) If the market clears, what is the equilibrium price of grain? What would it cost an individual farmer to produce one additional bushel of grain per week? Explain why the answers to these two questions are the same. Equilibrium price is 5. Since Supply is the horizontal sum of individual producers marginal cost schedule, the marginal cost of each and every farmer contributing to the total equilibrium output of 7 thousand bushels has a marginal cost of 5 it would cost each farmer $5 to produce an additional bushel of grain per week. b. (4 points) The government sets a target price of 9 but then lets the market determine the price. Consider the new equilibrium price and quantity. What would a feedlot (which produces beef) now pay for a bushel of grain to feed its cattle? What would it now cost an individual farmer to produce one additional bushel of grain per week? In light of your answers, is the new equilibrium quantity of grain efficient? EXPLAIN. (Remember that with a target price policy the government pays the farmers the difference between the target price and the price that actually results.) Total output would be 10 thousand bushels, and the market price, which a feedlot would pay, would be 2, although the marginal cost of producing grain (what it would cost a farmer to produce one more unit) would be 9. The last bushel produced cost more than anyone was willing to pay for it. In fact, the last 3 thousand bushels cost more to produce than consumers were willing to pay. Therefore the quantity produced is not efficient it is too high.
Economics 200 4 Scott c. (4 points) How will the target price policy affect the price of beef (grain is used in the production of beef)? Illustrate your answer with a diagram showing the supply and demand for beef. Is the new equilibrium quantity of beef efficient? EXPLAIN. Since the price of grain (an input in beef production) is artificially depressed because of the price target policy, the supply of beef will increase (supply curve will shift downward/outward) and the equilibrium price will fall and equilibrium quantity will increase. The supply of beef will be inefficient (too high) because the new supply schedule does not accurately/fully reflect the cost of the resources (the grain) used to produce the beef. d. (4 points) What is the elasticity of demand over the stretch of the demand curve from the point (Q=3, P=9) to the point (Q=10, P=2)? Explain simply by showing the appropriate formula and your work to get the numerical answer. Use arc elasticity: ( Q/ P)(P1 + P2)/(Q1 + Q2) = (7/( 7))(11)/(13) = 11/13, which is less than 1 (demand is inelastic). e. (4 points) Does your calculation in part d accurately predict the change in total revenue? Explain. Since we used arc elasticity, we will be able to accurately predict the change in revenue: Since demand is inelastic, a drop in price should result in a drop in total revenue. Indeed 3 x 9 = 27, which is more than 10 x 2 = 20. 5. Consumer Equilibrium, Pareto Efficiency. Two consumers (A and B) each have an income of 100. Each spends all of her income on two goods, X and Y. Each consumer maximizes utility subject to her budget constraint. The price of good X is 10 and the price of good Y is 5. At these prices, Consumer A consumes 4 units of X, and Consumer B consumes 8 units of X in equilibrium. a. (4 points) Draw two diagrams, one for Consumer A and one for Consumer B, showing the equilibrium (budget lines and indifference curves) for each consumer. Both budget constraints have y-intercepts of 100/5 = 20 and x-intercepts of 100/10 = 10. For consumer A, the budget constraint is tangent to an indifference curve at x = 4 and (therefore) y = (100 (4)(10))/5 = 12. For consumer B, the budget constraint is tangent to an indifference curve at x = 8 and (therefore) y = (100 (8)(10))/5 = 4.
Economics 200 5 Scott b. (4 points) In equilibrium, how many units of Y does Consumer A consume? How many units of Y does Consumer B consume? Show your work. 12 units for A and 4 units for B. See above. c. (4 points) In equilibrium, what is Consumer A s marginal rate of substitution (MU X /MU Y )? What is Consumer B s marginal rate of substitution? Briefly explain how you arrive at your answer (you do NOT need to provide intuition here). Both consumers face the same prices. Therefore, in equilibrium, both have the same MRS, equal to Px/Py = 2. d. (4 points) Consumer B obtains a coupon for good X, which allows her to buy as much as she wants for HALF PRICE. In your diagram for Consumer B, draw her new budget constraint and indifference curve, assuming that she now buys 14 units of X. What is Consumer B s marginal rate of substitution now? (Consumer A does not have the coupon, so she still buys the same quantities of X and Y). B s new budget constraint has the same y-intercept as the old, but the x-intercept is now 100/5 = 20. The new tangency is at x = 14 and y = (100 70)/5 = 6. B s MRS is now Px/Py = 5/5 = 1. e. (4 points) Consider the distribution of goods X and Y between consumers A and B under the assumptions of part d. Is this distribution Pareto efficient? EXPLAIN. No! The consumers face different prices and therefore have different marginal rates of substitution. A is willing to give up 2 units of Y for 1 of X while B is willing to give up 1 unit of X for 1 of Y. If B gives one unit of X to A in exchange for between one and two units of Y, both will be better off.
Economics 200 6 Scott 6. Production Possibilities, Opportunity Costs, and Gains from Trade. The diagrams below show the production possibilities frontier (PPF) for Country A and for Country B. The outcome with autarky (no trade) for each country is shown as point Z on each country's PPF. Good Y 4000 PPF for Country A with Z = (500, 2000) 2000 Z 500 1000 Good X Good Y 2000 PPF for Country B with Z = (1000, 1000) 1000 Z 1000 2000 Good X ***SHORT ANSWERS ONLY NO NEED TO WRITE EXPLANATION*** a. (1 point) Country A has an absolute advantage in the production good. Y b. (1 point) Country A has a comparative advantage in the production good. Y c. (1 point) Country B has an absolute advantage in the production of good. X d. (1 point) Country B has a comparative advantage in the production good. X e. (4 points) Suppose that after free trade that causes gains from trade, Country A produces 100 more of one of the goods, while Country B produces 75 more of the other good. After the trade, the total output of good Y is how much, while the total output of good X is how much? If trade produces gains, A must specialize in Y and B must specialize in X. Therefore A will produce 2000 + 100 = 2100 of Y and 500 25 = 475 of X, and B will produce 1000 + 75 = 1075 of X and 1000 75 = 925 of Y. The total output of X is therefore 475 + 1075 = 1550.