Microeconomics Exam: Consumer Choice, Cost Minimization, and Trade - Prof. William M. Boal | Exams Microeconomics

Intermediate Microeconomic Analysis Signature:

(Econ 173)

Printed name:

Drake University, Spring 1998

William M. Boal ID number:

FINAL EXAMINATION

May 12, 1998

PLEASE CHOOSE A CODE NAME: Final exam scores and course grades will be posted at the class

web site. But federal law prohibits posting grades by name or social security number. Please choose a

code name for yourself, like "Superman" or "Bill Clinton." The more unique the code name, the better.

My preferred code name is:

INSTRUCTIONS: This exam is closed-book, closed-notes, but calculators are permitted. Numerical

answers, if rounded, must be correct to at least 3 significant digits. Please write all answers in the blue

exam book in order. Show your work and circle your final answers . Point values for each question are

noted in brackets. Maximum total points are 100.

I. Your choice: Answer question (1) or question (2) but not both.

(1) [Consumer choice: 15 pts] Suppose Fred Fastfood has utility function U(q1,q2) = q11/2 + 2q21/ 2 ,

where q1 is the quantity of hamburgers eaten per month and q2 is the quantity of pizzas eaten per month.

Fred has $84 per month to spend on the two goods. The price of hamburgers is $2 each and the price of

pizzas is $6 each.

a. Give an equation for FredÕs budget line.

b. Compute the slope of FredÕs budget line, with hamburgers (q1) on the vertical axis and pizzas

on the horizontal axis. How many hamburgers must Fred give up to get one more pizza?

c. Give an expression for FredÕs marginal rate of substitution in consumption of pizzas for

hamburgers--that is, the slope of FredÕs indifference curve with hamburgers (q 1) on the vertical

axis and pizzas (q2) on the horizontal axis.

d. Are FredÕs preferences characterized by a diminishing marginal rate of substitution? Why or

why not?

e. Compute the number of hamburgers (q1) and pizzas (q2) Fred will choose per month.

(2) [Cost minimization: 15 pts] Suppose Big Muddy Ditchdiggers (BMD) has daily production function

q = 5 x11/2 x21/2 , where x1 is the number of backhoes and x2 is the number of workers employed per day.

a. Does BMD enjoy increasing returns to scale, decreasing returns to scale, or constant returns to

scale? Justify your answer.

b. Give an expression for BMDÕs marginal rate of substitution in production of workers for

backhoes--that is, the slope of BMDÕs isoquant with backhoes (x1) on the vertical axis and

workers (x2) on the horizontal axis.

Suppose BMD faces a rental rate for backhoes of w1 = $400 per day and a worker wage rate of w2 = $100

per day. Suppose further that BMD wishes to dig q = 50 ditches at least cost.

c. Compute the slope of BMDÕs isocost lines with backhoes (x1) on the vertical axis and workers

(x2) on the horizontal axis.

d. Compute the number of backhoes (x1) and workers (x2) that BMD should hire.

e. Compute BMDÕs total cost of digging 50 ditches, TC(50).

II. Do all: Answer all questions in this section.

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Intermediate Microeconomic Analysis Signature: (Econ 173) Printed name: Drake University, Spring 1998 William M. Boal ID number:

FINAL EXAMINATION

May 12, 1998

PLEASE CHOOSE A CODE NAME: Final exam scores and course grades will be posted at the class web site. But federal law prohibits posting grades by name or social security number. Please choose a code name for yourself, like "Superman" or "Bill Clinton." The more unique the code name, the better. My preferred code name is: INSTRUCTIONS: This exam is closed-book, closed-notes, but calculators are permitted. Numerical answers, if rounded, must be correct to at least 3 significant digits. Please write all answers in the blue exam book in order. Show your work and circle your final answers. Point values for each question are noted in brackets. Maximum total points are 100.

I. Your choice: Answer question (1) or question (2) but not both.

(1) [Consumer choice: 15 pts] Suppose Fred Fastfood has utility function U(q 1 ,q 2 ) = q 1 1/2^ + 2q 2 1/2^ ,

where q 1 is the quantity of hamburgers eaten per month and q 2 is the quantity of pizzas eaten per month. Fred has $84 per month to spend on the two goods. The price of hamburgers is $2 each and the price of pizzas is $6 each. a. Give an equation for FredÕs budget line. b. Compute the slope of FredÕs budget line, with hamburgers (q 1 ) on the vertical axis and pizzas on the horizontal axis. How many hamburgers must Fred give up to get one more pizza? c. Give an expression for FredÕs marginal rate of substitution in consumption of pizzas for hamburgers--that is, the slope of FredÕs indifference curve with hamburgers (q 1 ) on the vertical axis and pizzas (q 2 ) on the horizontal axis. d. Are FredÕs preferences characterized by a diminishing marginal rate of substitution? Why or why not? e. Compute the number of hamburgers (q 1 ) and pizzas (q 2 ) Fred will choose per month. (2) [Cost minimization: 15 pts] Suppose Big Muddy Ditchdiggers (BMD) has daily production function

q = 5 x 1 1/2^ x 2 1/2^ , where x 1 is the number of backhoes and x 2 is the number of workers employed per day.

a. Does BMD enjoy increasing returns to scale, decreasing returns to scale, or constant returns to scale? Justify your answer. b. Give an expression for BMDÕs marginal rate of substitution in production of workers for backhoes--that is, the slope of BMDÕs isoquant with backhoes (x 1 ) on the vertical axis and workers (x 2 ) on the horizontal axis. Suppose BMD faces a rental rate for backhoes of w 1 = $400 per day and a worker wage rate of w 2 = $ per day. Suppose further that BMD wishes to dig q = 50 ditches at least cost. c. Compute the slope of BMDÕs isocost lines with backhoes (x 1 ) on the vertical axis and workers (x 2 ) on the horizontal axis. d. Compute the number of backhoes (x 1 ) and workers (x 2 ) that BMD should hire. e. Compute BMDÕs total cost of digging 50 ditches, TC(50).

II. Do all: Answer all questions in this section.

Drake University, Spring 1998 Page 2 of 4 (3) [Welfare analysis of international trade: 9 pts] Suppose the domestic market for pocket calculators in Country X of is characterized by the following demand and supply curves:

Supply: QS = 200 P - 200 Demand: QD = 700 - 100 P

a. Compute the equilibrium price and quantity in the absence of international trade. Now suppose the pocket calculator industry is opened to free international trade, and the world price of pocket calculators turns out to be $. b. Will this country now import or export pocket calculators? How many? c. Will international trade create social welfare gain or social deadweight loss for Country X? How much? (4) [Monopoly, imperfect competition: 24 pts] Suppose the market for hot dogs at a particular beach is served by two stands (#1 and #2) with identical, constant marginal cost given by MC = AC = $2. Daily

market demand is given by P = 5 - Q/50, where Q = total hot dogs sold and P = price. Consider the

consequences of alternative models of seller interaction. First, suppose the two hot dog stands engage in price competition. a. Compute the equilibrium total hot dogs sold Q* and price P. b. Compute social deadweight loss. Second, suppose the two hot dog stands collude to maximize the sum of their profits. c. Find an expression for the market marginal revenue function MR(Q). d. Compute the hot dog stands’ total hot dogs sold Q and price P. e. Compute social deadweight loss. Third, suppose the two hot dog stands act as a (symmetric) Cournot duopoly , each setting its own quantity to maximize its own profits, while taking the other stand’s quantity as given. Let q 1 denote stand #1’s quantity of hot dogs sold and q 2 denote stand #2’s quantity, so that Q = q 1 + q 2. f. Find an expression for stand #1’s reaction function , showing the quantity that stand #1 will produce for any given quantity sold by stand #2: q 1 * = f(q 2 ). g.. Compute the equilibrium total hot dogs sold Q and price P*. h. Compute social deadweight loss.

Drake University, Spring 1998 Page 4 of 4 e. Given your answers above, what will happen to the market for insurance? Justify your answer. (8) [Public goods: 15 pts] Five neighbors live in houses surrounding a public park. The park is quite attractive but it has no trees. Trees cost $20 each. Each neighborÕs demand (or marginal benefit) for

trees is given by P = 25 - Q, where P denotes marginal benefit and Q denotes the number of trees in the

park. Note that each tree is enjoyed simultaneously by all five neighbors a. Suppose one neighbor, taking initiative, decides to buy some trees for the park. How many will that neighbor buy? b. After that first neighbor bought and planted these trees, will the other neighbors buy additional trees? Why or why not? c. Compute the economically efficient (or socially optimal) number of trees for the park. d. Compute the deadweight loss in the absence of coordination between the neighbors. In other words, compute the deadweight loss implied by your answers to (a) and (b). e. Suppose the houses and the park were privately owned by a landlord who charged rent to the neighbors. How many trees would the landlord buy and plant? Justify your answer.

IV. Your choice: Answer essay question (9) or essay question (10) but not both.

(9) [13 pts] Suppose new firms can enter or exit an industry freely. a. Does free entry and exit imply average-cost pricing (that is, zero economic profits) in the long run? Put differently, must the long-equilibrium price equal average cost? Why or why not? b. Does free entry and exit imply marginal-cost pricing in the long run? Put differently, must the long-run equilibrium price equal marginal cost? Why or why not? (10) [13 pts] In developing the models of consumer demand and labor supply, we used the same set of assumptions about preferences (transitivity, monotonicity, diminishing marginal rate of substitution, and normal goods). Using these assumptions, we showed on the one hand that consumer demand must have negative slope. On the other hand, labor supply could have negative or positive slope or could even be vertical. Why were we able to derive a definite result for consumer demand but not for labor supply? [end of exam]

Microeconomics Exam: Consumer Choice, Cost Minimization, and Trade - Prof. William M. Boal, Exams of Microeconomics

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Download Microeconomics Exam: Consumer Choice, Cost Minimization, and Trade - Prof. William M. Boal and more Exams Microeconomics in PDF only on Docsity!

FINAL EXAMINATION

May 12, 1998

I. Your choice: Answer question (1) or question (2) but not both.

(1) [Consumer choice: 15 pts] Suppose Fred Fastfood has utility function U(q 1 ,q 2 ) = q 1 1/2^ + 2q 2 1/2^ ,

q = 5 x 1 1/2^ x 2 1/2^ , where x 1 is the number of backhoes and x 2 is the number of workers employed per day.

II. Do all: Answer all questions in this section.

Supply: QS = 200 P - 200 Demand: QD = 700 - 100 P

market demand is given by P = 5 - Q/50, where Q = total hot dogs sold and P = price. Consider the

trees is given by P = 25 - Q, where P denotes marginal benefit and Q denotes the number of trees in the

IV. Your choice: Answer essay question (9) or essay question (10) but not both.