Microeconomics I 2011/12

Transcription

1 October 25, 2011 Undergraduate Programs Business Administration and Economics Microeconomics I 2011/12 Duration: 2h15m + 30 min Fernando Branco, Fernando Machado (Professors), Bruno Pereira, Daniel Horta, Duarte Ribeiro, João Coelho and Nuno Clara. A. This exam has 5 groups of questions. PLEASE READ BEFORE YOU START B. You must start with group I (multiple choice questions, provided in a separate sheet): a. You have 25 minutes to complete it. After that time the answer sheet for that group will be collected. b. In this group, if you check a wrong option you will get a penalty (equal to one fourth of the question s total marks). C. Please provide your answers to Groups II, III, IV e V in separate sheets. II (3.5 points) 1. During his first year at the University, John bought 8 new textbooks at a cost of 50 each. He did not buy any used books, whose cost is 30 each. When the University bookstore announces a 20% increase in new textbooks and a 10% increase in used textbooks for the next year, John s father offers him 80 extra. Is John better off, the same or worse off after the price change? Briefly explain, using a diagram. 2. Suppose that McDollar s is the only restaurant offering hamburgers in a certain village. McDollar s price for a meal was 5. At that price the restaurant used to serve on average 1500 meals per month. Suppose now that McDollar s was sued by a well-known fast food multinational that happens to have a similar name. The court decided that McDollar s should align its name with the multinational and start paying that company a monthly franchise fee. As a result of the court s decision, the owner of McDollar s is considering whether he should close down his restaurant (if he decides to do so, he will start a new clothing store named Massimo Kuti) or perhaps re-think his pricing strategy. One friend told him that he should raise prices in order to recover the added cost of the franchise fee, but another one told him exactly the opposite - reduce prices in order to attract more customers and increase revenue. As a microeconomics specialist, what advice would you give to this innovative entrepreneur? Be short and concise. 1

2 III (4.5 points) John has some preferences over ice-creams (good X) and meals (good Y). His utility function can be described by: U=0,7ln(X)+0,3ln(Y) a) Find the demand functions for ice-creams and meals. If the price of ice-creams increases by 1%, by how much does the consumption of ice-creams change? John has a monthly income of 100 monetary units (m.u.) which he spends on the two goods. Suppose that the price of ice-creams is 4 m.u. and the price of meals is 2 m.u.. Additionally suppose that the ice-cream shop does not allow John to buy more than 10 ice-creams a month. b) Represent graphically John s budget constraint. What is the optimal consumption bundle? c) John s friend, Ana, also has some preferences over ice-creams and meals. Her preferences are such that she is always willing to change 1 unit of ice-cream for 3 units of meals (regardless of the market price). Ana has bought 10 ice-creams. C1) Will John and Ana make any exchange if they meet? (Suggestion: you may want to explain your answer with a diagram). C2) What is John s new optimal bundle? IV (4.5 points) Microeconomics courses are one important factor that guarantees a steady demand for calculators year after year. Admit that the short run cost function to produce scientific calculators (X), the preferred instrument among Microeconomics teachers, is given by: C ( ) ( ) SR X = wx K + + rk and r are the prices of labor and capital, respectively, and K is the short run level of capital. 1 1, where w a) Determine the long run cost function. Show that if a firm installs the optimal capital level, it implies that there is a minimum scale of production, which increases if capital gets relatively more expensive. Ignore the previous information and consider now that the production of new graphing calculators (Y), very popular among Microeconomics students, is characterized by the function: {( 2K 20) L} Y = min,, with K 10 (Y is zero for K<10). Looking at the technology involved, the government reached the conclusion that small companies producing graphing calculators were hiring relatively few workers. Concerned with the unemployment rate in the economy, the government imposed on all firms that they would need to employ at least one unit of labor for each unit of capital. b) Draw the isoquants that correspond to producing 10 and 30 graphing calculators. Starting from the analysis of those two isoquants, comment on this policy s effectiveness in stimulating the employment by small firms. c) Compute the long run cost function of producing graphing calculators. 2

3 V (3.5 points) Fat & Juicy is a small firm in a competitive market composed by 100 identical firms with similar technologies of production that sells frozen Italian food (Q). The market demand for frozen Italian food is: Q D (P)=700-P and the average total cost of Fat & Juicy is: ATC(q i )=10q i +100+FC/q i a) Determine the aggregate short-run supply curve of the frozen Italian food market and identify below which Fixed Cost (FC) Fat & Juicy should operate in the short-run. b) Concerned about the budget balance, the government decided to impose a new tax on suppliers so that the price paid by consumers will be 25% higher than the net price received by suppliers. The government claims that total welfare will not be affected, since tax revenues will compensate for all losses consumers and suppliers will face. Can you prove (quantitatively) that the government is wrong? Illustrate your answer graphically. [use Q S (P)=5P-500 as the market supply if you did not complete the previous question] Good Luck! 3

4 Microeconomics I October Name: Number: 1. A decrease in income will not lead to: a) A movement along the demand curve. b) A leftward shift of the demand curve. c) A rightward shift of the demand curve. d) All of the above. I. Multiple choice questions (4.0 points) 2. If the slope of the indifference curve is steeper than the slope of the budget line, and X is on the horizontal axis: a) The consumer is willing to give up more of good Y to get an additional unit of good X than is necessary under the current market prices. b) MRS < P X /P Y. c) MRS < - P X /P Y. d) The consumer is willing to give up more of good X to get an additional unit of good Y than is necessary under the current market prices. 3. Total product begins to fall when: a) Marginal product is maximized. b) Average product is maximized. c) Marginal product is zero. d) Average product is zero. 4. A firm might choose to produce its own inputs if: a) Specialized investment is not important. b) Long-term contracts are costly to write. c) The exchange environment is not complex. d) Spot markets for the input exist. 5. Which of the following is necessarily true under monopoly in the short run? a) Profits are always positive. b) P > minimum of ATC. c) P = MR. d) None of the statements above are correct. 6. You are the manager of a gas station and your goal is to maximize profits. Based on your past experience, the elasticity of demand by civil servants for a car wash is -6, while the elasticity of demand by non-civil servants for a car wash is -4. If you charge non civil servants 20 for a car wash, how much should you charge civil servants for a car wash? a) 15. b) 18. c) 20. d) There s insufficient information to answer. 7. A firm that operates in a perfectly competitive market is selling 150 units of output per week at a price of 10. Average total cost is 10, average variable cost is 8 and marginal cost is 11. Based on this information we know that the firm: a) Can increase profit by increasing its weekly level of output. b) Can increase profit by reducing its weekly level of output. c) Can increase profit by selling at a higher price. d) None of the statements above are correct. 1

5 1. A decrease in income will not lead to: a) A movement along the demand curve.* b) A leftward shift of the demand curve. c) a rightward shift of the demand curve. d) All of the above. Solutions I. Multiple choice questions (4.0 points) 2. If the slope of the indifference curve is steeper than the slope of the budget line, and X is on the horizontal axis: a) The consumer is willing to give up more of good Y to get an additional unit of good X than is necessary under the current market prices.* b) MRS < P X /P Y c) MRS < - P X /P Y d) The consumer is willing to give up more of good X to get an additional unit of good Y than is necessary under the current market prices. 3. Total product begins to fall when: a) Marginal product is maximized. b) Average product is maximized. c) Marginal product is zero.* d) Average product is zero. 4. A firm might choose to produce its own inputs if: a) Specialized investment is not important. b) Long-term contracts are costly to write.* c) The exchange environment is not complex. d) Spot markets for the input exist. 5. Which of the following is necessarily true under monopoly in the short run? a) Profits are always positive. b) P > minimum of ATC. c) P = MR d) None of the statements above are correct.* 6. You are the manager of a gas station and your goal is to maximize profits. Based on your past experience, the elasticity of demand by civil servants for a car wash is -6, while the elasticity of demand by non-civil servants for a car wash is -4. If you charge non civil servants 20 for a car wash, how much should you charge civil servants for a car wash? a) 15. b) 18.* c) 20. d) There s insufficient information to answer. 7. A firm that operates in a perfectly competitive market is selling 150 units of output per week at a price of 10. Average total cost is 10, average variable cost is 8 and marginal cost is 11. Based on this information we know that the firm: a) Can increase profit by increasing its weekly level of output. b) Can increase profit by reducing its weekly level of output.* c) Can increase profit by selling at a higher price. d) None of the statements above are correct. 1

6 II (3.5 points) 1. During his first year at the University, John buys 8 new textbooks at a cost of 50 each. He did not buy any used books, whose cost is 30 each. When the University bookstore announces a 20% increase in new textbooks and a 10% increase in used textbooks for the next year, John s father offers him 80 extra. Is John better off, the same or worse off after the price change? Explain using a diagram. Given the price ratio and John s preferences, his optimal point in the first year is a corner solution (8 new books and 0 used books). By doing some simple calculations one can conclude that the prices of new books increased from 50 to 60, while the price of used books increased from 30 to 33 in the second year. On the other hand, John s total budget for textbooks increased from 400 to 480. It is obvious that John s budget increase (80 ) is enough for him to afford the original bundle (8 new books * 10 increase=80 ). Therefore, John cannot be worse off. However, he may be better off. Since the price of used books has increased less in percentage terms than income (and the price of new books), there is as expansion of the budget set, as shown below: Used 480/33 400/30 B 8 A New John s preferences are such that in the initial situation the optimal point is A (corner solution). At that point we must have MRS P N /P U. Due to changes in prices and in income, the budget constraint rotates around the X intercept and the budget set expands. Depending on John s preferences, the optimal point may stay at A or move to an interior point such as B (as shown in this case). Therefore we can conclude that in the second year John may be the same or better off, but not worse off. Additional note: Different assumptions could be made about John s preferences. For example, some students have assumed linear preferences, in which case the indifference curves would be straight lines. In that scenario the optimal point would remain at A or move to the opposite corner (that is, John would only buy used books in the second year). In any event, the main conclusion would still be valid (John may be the same or better off in the second year, but not worse off). 2

7 2. Suppose that McDollar s is the only restaurant offering hamburgers in a certain village. McDollar s price for a meal was 5. At that price the restaurant used to serve on average 1500 meals per month. Suppose now that McDollar s was sued by a well-known fast food multinational that happens to have a similar name. The court decided that McDollar s should align its name with the multinational and start paying that company a monthly franchise fee. As a result of the court s decision, the owner of McDollar s is considering whether he should close down his restaurant (if he decides to do so, he will start a new clothing store named Massimo Kuti) or perhaps re-think his pricing strategy. One friend told him that he should raise prices in order to recover the added cost of the franchise fee, but another one told him exactly the opposite - reduce prices in order to attract more customers and increase revenue. As a microeconomics specialist, what advice would you give to this innovative entrepreneur? Be short and concise. Being the only fast food restaurant in the Village, one can assume that McDollar s has a significant level of monopoly power and is able to charge prices above marginal cost. Under those conditions, the optimal price results from the application of the rule MC=MR. The new monthly franchise fee is clearly a fixed cost (in this case a fixed cost that the firm will have to pay even in the long run). Since fixed costs do not have any impact on marginal cost, the restaurant s optimal price will not be affected by the franchise fee. Therefore, there is no reason to change the restaurant s pricing. However the franchise fee increases total cost and consequently reduces profits. If the restaurant ceases to have positive profits over the long run, then the best option is to close down. To conclude, the restaurant s owner should do one of two things: - Close down the restaurant, if the fixed fee is high enough to cause negative profits. - Stay in business and maintain the price policy, if profits are still positive. Note: The above analysis assumes, of course, that the demand faced by the firm is not affected. One could argue that the change in the restaurant s name would lead to an increase in demand, but that was not the main issue here. III (4.5 points) John has some preferences over ice-creams (good X) and meals (good Y). His utility function can be described by: U=0,7ln(X)+0,3ln(Y) a) Find the demand functions for good Y and for good X. If the price of X increases by 1%, by how much does the consumption of X change? 0, 7* M x D = Px y D = 0,3* M Py ε x, p = x Px 0, 7* M = p x x Px 2 Px 0, 7* M / Px = 1 John has a monthly income of 100 monetary units (m.u.) which he spends on the two goods. Suppose that the price of ice-creams is 4 m.u. and the price of meals is 2 m.u.. Additionally suppose that the ice-cream shop does not allow John to buy more than 10 ice-creams a month. b) Represent graphically John s budget constraint. What is the optimal consumption bundle? 3

8 y x If there was no constraint on the amount of x consumed the optimum would be: X=17,5 Y=15 However as that point is not possible we will have a corner solution: (x,y)=(10,30) U=2, c) John s friend, Ana, also has some preferences over ice-creams and meals. Her preferences are such that she is always willing to change 1 unit of ice-cream for 3 units of meals (regardless of the market price). Ana has bought 10 ice-creams. C1) Will John and Ana make any exchange if they meet? (Suggestion: you may want to explain your answer with a diagram). If Ana gives John one ice-cream and John gives Ana 3 meals, Ana will stay indifferent and John will have the bundle: (x,y)=(11,27), which allows him to get an utility of U=2,66, so they ll trade. C2) What is John s new optimal bundle? Ana is always willing to change 1 of x for 3 of y so she is giving John a price ratio of (Px/Py)=3 John income is now given by: M=10Px+30Py=10*3+30=60 John therefore solves the problem: MRS=3 x(px/py)+y=60 (0,7y)/(0,3x)=3 3x+y=60 x=14 y=18 U=2,71 4

9 IV (4.5 points) a) Long run cost function and minimum scale of production The long run cost function can be found by finding the optimal capital level and substituting it into the short run cost function: dc SR d K C LR = 0 K = w r X w r 1 1 ( X ) = wx X r X 1 = 2 wrx r w r To find the minimum scale of production one needs to determine when the optimal capital level is non-negative: K w = X 1 0 r X r w b) Isoquants K 25 Y =30 15 Y = L The isoquant that corresponds to an output of 10 units violates the government s imposition because the firm would be using more capital than labor. If one determines the intersection of the efficient line of the Leontief function with the line (L=K), one can find that for outputs lower than 20 units, the government s rule will be binding. Hence, small companies (producing less than 20 units) will need to employ more labor than they would do without the restriction. 5

10 c) Long run cost function For Y 20: The rule does not constrain the firms, because they use more than one unit of labor per unit of capital. Y + 20 Y = 2K 20 K = 2 Y = L L = Y Y + 20 C( Y ) = wy + r 2 For Y<20: Firms will use K=L. Capital will be the factor constraining the Leontief function. Therefore, Y + 20 = K = L 2 Y + 20 Y + 20 C( Y ) = w + r = 2 2 Y ( w + r) Total cost function: Y + 20 ( w + r) 2 C ( Y ) = Y + 20 wy + r 2 Y < 20, Y 20 6

11 V (3.5 points) Fat & Juicy is a small firm in a competitive market composed by 100 identical firms with similar technologies of production that sells frozen Italian food (Q). The market demand for frozen Italian food is: Q D (P)=700-P and the average total cost of Fat & Juicy is: ATC(q i )=10q i +100+FC/q i a) Determine the aggregate short-run supply curve of the frozen Italian food market and identify below which Fixed Cost (FC) Fat & Juicy should operate in the short-run. a) TC(Q)=10Q Q+CF MC(Q)=20Q+100 AVC(Q)=10Q+100 Q i =0.05P-5 Q S (P)=5P-500 (P 100) In the short-run the firm should operate regardless of the fixed costs since price exceeds the average variable cost and, therefore, each unit sold generates more revenue than the variable cost of producing that same unit. The firm should continue to operate in the short-run, otherwise would realize a loss equal to the fixed costs. b) Concerned about the budget balance, the government decided to impose a new tax on suppliers so that the price paid by consumers will be 25% higher than the net price received by suppliers. The government claims that total welfare will not be affected, since tax revenues will compensate for all losses consumers and suppliers will face. Can you prove (quantitatively) that the government is wrong? Illustrate your answer graphically. [use Q S (P)=5P-500 as the market supply if you did not complete the previous question] b) P S(Pc) Without tax P=200 Q=500 CS= PS= W= With tax (1.25Pp=Pc) Pc=240 Pp=192 Q=460 CS= (-19200) PS= (- 3840) S(Pp) D(Pc) Q A tax revenue of will not compensate for the decrease in CS and PS (of ), since there is a dead weight loss of