Microeconomic Intermediate Analysis (Econ 173) Drake University, Fall 2007 William M. Boal
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FINAL EXAMINATION VERSION A December 19, 2007
INSTRUCTIONS: This exam is closed-book, closed-notes. Simple calculators are permitted, but not graphing calculators or calculators with alphabetical keyboards. Point values for each question are noted in brackets. As usual in this course, "exp(x)" denotes the exponential function (also written ex ) while "ln(x)" denotes the natural logarithm function (logarithm to base e = 2.7182818...). I. MULTIPLE CHOICE: Circle the one best answer to each question. Feel free to use margins for scratch work. [3 pts each--99 pts total] The next question refers to the following graph of consumer bundles. The next question refers to the following graph of four possible indifference curves.
A B Food C D Other goods
(1) According to the assumption of "monotonicity" or "more is better," which bundle is surely preferred by any consumer to bundle E? a. Bundle A. b. Bundle B. c. Bundle C. d. Bundle D. e. Bundles A,C, and D. f. All of the above.
(2) Which indifference curve above violates the assumption of diminishing marginal rate of substitution? a. Curve A. b. Curve B. c. Curve C. d. Curve D. e. None of the above.
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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The next two questions refer to the following graph of a consumer's budget line and indifference curves. Suppose the consumer is currently at bundle A.
Other goods = q1 A Energy = q2 (3) This consumer could enjoy higher utility, without increasing total spending, by a. purchasing less energy and more other goods. b. purchasing more energy and fewer other goods. c. purchasing less energy and fewer other goods. d. any of the above. e. none of the above. (4) Let MU1 denote the marginal utility of other goods and MU2 the marginal utility of energy for this consumer. Let p1 denote the price of other goods and p2 denote the price of energy. At bundle A, a. MU2/MU1 = p2/p1 . b. MU2/MU1 < p2/p1 . c. MU2/MU1 > p2/p1 . d. MU2 = MU1 and p2 = p1 . e. cannot be determined from information given. The next four questions refer to the graph below. Assume the consumer's income is $60.
(5) The old price of energy was a. $2. b. $5. c. $10. d. $12. e. $15. f. $20. g. $25. (6) The new price of energy is a. $2. b. $5. c. $10. d. $12. e. $15. f. $20. g. $25. (7) The substitution effect alone of the price change causes the quantity demanded of energy to decrease by a. one unit. b. two units. c. three units. d. four units. e. five units.
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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(8) The income effect alone of the price change causes the quantity demanded of energy to decrease by a. one unit. b. two units. c. three units. d. four units. e. five units. The next three questions refer to the following information. Suppose that the price of milk increases by 5% and that the price elasticity of demand for milk is 0.6 . (9) The quantity of milk consumed will a. increase by about 5%. b. increase by about 3%. c. increase by about 2%. d. increase by about 1%. e. remain unchanged. f. decrease by about 1%. g. decrease by about 2%. h. decrease by about 3%. i. decrease by about 5%. (10) The amount of money consumers spend on milk will a. increase by about 5%. b. increase by about 3%. c. increase by about 2%. d. increase by about 1%. e. remain unchanged. f. decrease by about 1%. g. decrease by about 2%. h. decrease by about 3%. i. decrease by about 5%. (11) On the basis of milk's price elasticity of demand, the demand for milk would be classified in economics as a. perfectly elastic. b. elastic. c. unitary elastic. d. inelastic. e. perfectly inelastic.
(12) The production function q = 2 x13/4 x21/2 shows a. constant returns to scale. b. decreasing returns to scale. c. increasing returns to scale. d. cannot be determined from the information given. The next two questions refer to the following diagram of a firm's isocost lines and an isoquant. Suppose the firm is currently at input combination A.
Machines
A Workers (13) This firm could lower its total cost, without reducing output, by a. using fewer machines and more workers. b. using more machines and fewer workers. c. either (a) or (b). d. neither (a) nor (b). e. cannot be determined. (14) Let MP1 denote the marginal product of machines and MP2 the marginal product of workers for this firm. Let w1 denote the price of machines and w2 denote the price of workers. At input combination A, a. MP2/MP1 < w2/w1 . b. MP2/MP1 > w2/w1 . c. MP2/MP1 = w2/w1 . d. MP2 = MP1 and w2 = w1 . e. cannot be determined from information given.
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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The next four questions refer to the following information. Suppose a firm's long-run total cost function is given by TC(q) = 0.5q3 50 q2 + 1270 q . (15) The firm's average cost function is AC(q) = a. 0.5 q3 50 q2 + 1270 q . b. 0.5 q2 50 q + 1270 . c. 1.5 q2 100 q + 1270 . d. 3 q 100 . e. q 50 . (16) The firm's marginal cost function is MC(q) = a. 0.5 q3 50 q2 + 1270 q . b. 0.5 q2 50 q + 1270 . c. 1.5 q2 100 q + 1270 . d. 3 q 100 . e. q 50 . (17) The firm's efficient scale of operation is a. qES = 10. b. qES = 20. c. qES = 30. d. qES = 40. e. qES = 50. f. qES = 60. g. qES = 70. h. qES = 80. (18) The lowest price at which this firm can produce output without making a loss is a. $10. b. $20. c. $30. d. $40. e. $50. f. $60. g. $70. h. $80.
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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The next two questions refer to the following graph, which shows supply and demand for a particular good. Suppose a tax of $3 per unit is placed on this good.
$12 $11 $10 $9 $8 $7 $6 $5 $4 $3 $2 $1 $0 0 10 20 30 40 50 60
The next three questions refer to the following graph of an economy's production-possibility curve. Assume this economy is in general competitive equilibrium at point A, where the slope of the production-possibility curve is 4 (in absolute value).
Other goods
Price
A
DemandQuantitySupply
Energy
(19) As a result of the tax, which decreases? a. Consumer surplus. b. Producer surplus. c. Both of the above. d. None of the above. (20) The deadweight social loss from the tax is a. $2. b. $3. c. $5. d. $10. e. $15. f. $20. g. $25. h. $30.
(21) If this economy were to produce two more units of energy, it would have to reduce production of other goods by about a. one unit. b. two units. c. four units. d. six units. e. eight units. (22) If the price of energy in this economy is $4 per unit, then the price of other goods must be a. $1. b. $2. c. $4. d. $8. e. $16. The next question refers to the graph below of alternative average cost curves.
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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Assume that industry output is at least Q*.
f. $120.00. (26) Firm A and Firm B must together produce a total of 100 units of output. Firm A's marginal cost is given by MCA = 5 + (qA/10) , where qA denotes its own output level. Firm #B's marginal cost is given by MCB = 8 + (qB/4), where qB denotes its own output level. The output allocation that will minimize the total cost of both firms together is a. qA = 0 and qB = 100. b. qA = 20 and qB = 80. c. qA = 40 and qB = 60. d. qA = 50 and qB = 50. e. qA = 60 and qB = 40. f. qA = 80 and qB = 20. g. qA = 100 qnd qB = 0. (27) According to the model of symmetric Cournot oligopoly, the Lerner index will be lower, a. the more elastic is demand. b. the fewer firms are in the industry. c. both (a) and (b). d. neither (a) nor (b). (28) Unlike other taxes, a pollution tax (also called a Pigou tax) a. causes deadweight loss. b. does not generate any revenue for the government. c. affects only producers. d. does not cause deadweight loss. (29) An efficient way to distribute pollution permits is a. to sell them at auction. b. to allow them to be bought and sold by polluters. c. either of the above. d. to assign them by a lottery. (30) A beach can be enjoyed simultaneously by many people. However, it can be fenced and gated so that people must pay an admission charge. Thus a beach is
A Average cost B C
Quantity of output
Q*
(23) Which average cost curve above is typical of a firm that enjoys a natural monopoly? a. Average cost curve A. b. Average cost curve B. c. Average cost curve C. d. None of the above. e. Cannot be determined from information given. (24) Suppose a flower vendor with market power is now selling 7 bouquets per hour at a price of $10. If he cuts the price to $9.50, he can sell one more bouquet per hour (that is, a total of 8 bouquets per hour). The vendor's marginal revenue for the eighth bouquet is therefore a. - $0.50 . b. $1.00 . c. $6.00 . d. $9.50 . e. $10.00 . (25) Suppose the demand for a monopolist's product has an elasticity -6, of and the monopolist's marginal cost is $20. Then the profit-maximizing price is a. $6.00 . b. $16.67 . c. $24.00 . d. $30.00 . e. $60.00 .
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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a. a nonrival good. b. a nonexcludable good. c. both a nonrival good and a nonexcludable good. d. neither a nonrival good nor a nonexcludable good. (31) A risk-averse person's utility function shows a. increasing marginal utility of wealth (or income). b. constant marginal utility of wealth (or income). c. decreasing marginal utility of wealth (or income). d. none of the above. (32) Which utility function shows risk aversion?
a. b. c. d.
U(W) = 5 + 3W. U(W) = 2 W2. U(W) = 20 - 1/W. U(W) = 5W.
(33) Health insurance that covers the effects of AIDS is likely to attract a disproportionate number of AIDS sufferers. This problem is called a. adverse selection. b. moral hazard. c. perfect information. d. risk aversion.
II. PROBLEMS: Please write your answers in the boxes on this question sheet. Show your work and circle your final answers.
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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(1) [Budgets and choice: 12 pts] A consumer has the following utility function: U(q1,q2) = (q1-4) q2 , where q1 denotes the quantity of health care and q2 denotes the quantity of other goods. The price of health care is $10 and the price of other goods is $5. The consumer has $200 in income to spend on these items. a. [4 pts] Give an equation for the consumer's budget line. The variables q1 and q2 should be the only unknowns.
b. [4 pts] Find a formula for the consumer's marginal rate of substitution of other goods for health care--that is, the |slope| of the consumer's indifference curve with health care on the vertical axis and other goods on the horizontal axis. The variables q1 and q2 should be the only unknowns. Circle your final answer.
c. [4 pts] Solve for the quantities of health care (q1*) and other goods (q2*) that this consumer will choose. Circle your final answers.
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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(2) [Welfare analysis of tax: 16 pts] Suppose domestic demand and supply for a good are given by the following equations. Demand: QD = 800 100 P Supply: QS = 200 P 400. a. Compute the equilibrium price and quantity without international trade.
Suppose the market is opened to international trade and the world price turns out to be PW = $3. b. Will this country import or export this good? c. How much? d. Will consumer surplus increase or decrease? e. By how much? f. Will producer surplus increase or decrease? g. By how much? h. Compute the net gain to this country from international trade.
units
$
$ $
Price
Quantity
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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(3) [General equilibrium, exchange efficiency: 14 pts] Adam and Brianna like ice cream and cake. Adam's utility function is given by UA = q1A q2A, where q1A denotes the quantity of ice cream and q2A denotes the quantity of cake he eats. Brianna's utility function is given by UB = q1B2 q2B, where q1B denotes the quantity of ice cream and q2B denotes the quantity of cake she eats. a. [2 pts] Find a formula for Adam's marginal rate of substitution in consumption of cake for ice cream--that is, the slope of Adam's indifference curve with ice cream on the vertical axis and cake on the horizontal axis. MRSCA = b. [2 pts] Find a formula for Brianna's marginal rate of substitution in consumption of cake for ice cream--that is, the slope of Brianna's indifference curve with ice cream on the vertical axis and cake on the horizontal axis. MRSCB = [6 pts] There are a total of 30 scoops of ice cream and 30 pieces of cake available. Six examples of feasible allocations are given below. State whether each allocation is Pareto efficient or inefficient. Efficient or Adam Brianna inefficient? Allocation Ice cream Cake (q2A) Ice cream Cake (q2B) (q1A) (q1B)
C D E F G H
6 15 0 10 30 15
10 15 0 10 30 20
24 15 30 10 0 15
20 15 30 5 0 10
(i) [4 pts] Plot and label the above efficient allocations in the Edgeworth box below, and sketch the contract curve for Adam and Brianna. Ice cream
30 25 20 15 10 5 0
Brianna's origin
Adam's origin
0
5
10
15
20
25
30
Cake
Intermediate Microeconomic Analysis (Econ 173) Drake University, Fall 2006
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(4) [Cournot duopoly: 14 pts] Suppose two firms form a (symmetric) Cournot duopoly, each firm setting its own quantity while taking the other firm's quantity as given. Let q1 = firm #1's quantity and q2 = firm #2's quantity, so that total market quantity Q = q1 + q2 . The market demand curve is P = 19 (Q/100). Each firm has constant marginal and average cost equal to $1. Circle your final answers. Use the space on the next page for scratch work. Note: question continues on next page. a. Find an expression for firm #1's revenue, as a function of its own quantity and the quantity produced by the other firm: Rev1(q1,q2).
b. Find an expression for firm #1's marginal revenue, as a function of its own quantity and the quantity produced by the other firm: MR1(q1,q2).
c. Find an expression for firm #1's reaction function, showing how much firm #1 will produce for any given le...