MBA 710 Professor Malamud

MBA 710 Professor Malamud

Applied Economic Analysis February 10, 2005

Classroom Examination #1

You can rewrite one question at home after the exam is returned to you. If you choose to rewrite a question, you must rewrite ALL of the question, even parts that you got a perfect score on in class Rewrites are graded to a higher standard than answers written in class! The exact same answer may earn fewer points on the rewrite than on the exam taken in class. Your score for the exam is the average of your classroom score and your rewrite score. Rewrites are due February 24. You must submit your classroom exam together with your rewrite so your scores can be averaged.

You have plenty of room to answer the questions in the space provided. Do not feel that you have to use it all.

Question I (50 poiuynts)

Two poiuyt dealers are talking shop at the annual meeting of Purveyors of Poiuyts International (“Popeye”) in Las Vegas. “We both pay $100 for each poiuyt we import from China and resell locally,” the Los Angeles dealer tells the Seattle dealer. “But since you sell them at a higher price in Seattle ($200) than I get in Los Angeles ($150), the price elasticity of demand for poiuyts must be lower in Seattle than it is in Los Angeles.”

“No,” the Seattle dealer responds, “since each of us is maximizing profit in his local market, the price elasticities of demand in the two markets must be equal.”

a)  Who is right? Why? (25 poiuynts)

b)  Why might the price elasticities of demand for poiuyts differ in the two markets, if indeed they do differ? (25 poiuynts)

Question II (60 points)

Qwerts ‘R Us sells 100,000 qwerts per month at a price of $10 each. Its economic consultant, Marge N. L’Coste, estimates the price elasticity of demand for its product to be 2 at the output-price combination at which Qwerts ‘R Us is operating.

a)  If Qwerts ‘R Us wants to increase sales to 110,000 units per month, approximately what price should it charge? (15 points)

b)  Qwerts ‘R Us faces falling marginal revenue. Its marginal cost, however, is constant at $6 per qwert. Is the profit-maximizing output level for Qwerts ‘R Us greater than, less than, or precisely equal to the 100,000 units per month it is currently producing and selling? Explain why. (Just answer the question, don’t try to find the optimal output-price combination). (15 points)

Question II, continued

c)  Set up a spreadsheet and show the instructions you would give Solver to maximize Qwerts ‘R Us’s profits. Assume the demand for the company’s qwerts is linear in the range of interest.

i)  Let P equal the price of qwerts and Q equal the quantity of qwerts demanded at that price. Express Q as a function of P, assuming the demand relation is linear in the range of interest. (15 points)

ii)  Define the variables in this problem in Column A below and show how they are calculated in Column B. Also show the instructions you would give Solver to maximize profit. (15 points)

Solver Instructions:

Target Variable: ______Max ____ Min ____

By changing: ______

Subject to the constraint(s):

Question III (40 points)

A certain person who has no money at all has the following utility function

U(b,x,y) = (b + 20) x2/3 y5/3

where

b = loafs of bread he buys

x = dozens of eggs he buys

y = bottles of wine he buys.

The market prices of bread, eggs, and wine are $1 per loaf, $2 per dozen, and $10 per bottle, respectively, and his marginal utilities of bread, eggs, and wine are

MUb = U/(b +20)

MUx = (⅔)U/x

MUy = (5/3)U/y

a)  What values of b, x, and y maximize this person’s utility? (25 points)

b)  The optimal value of b turns out to be negative. Does this make sense? Why? (15 points)