Department of Agricultural Economics Texas A&M University AGEC 317, Fall

Fall 2013 AGEC 317 Capps

Problem Set #2

1 1 1. Verify the demand function. Q  p b , where a > 0, b> 0, has constant demand a elasticity. a) Verify the own-price elasticity of demand does not depend upon Q and p.

b) The parameters a and b of the demand function are restricted to be positive. Why?

2. Management of McPablo’s Food Shops has completed a study of weekly demand for its “old-fashioned” tacos in 53 regional markets. The study revealed that

Q  400 1,200P  0.8A  55Pop  800P 0 ,

where Q is the number of tacos sold per store per week, A is the level of local advertising expenditures (in dollars), Pop denotes the local population (in thousands), and P0 is the average taco price of local competitors. For the typical McPablo’s outlet, P = $1.50, A = $1,000, Pop = 40, and P0 = $1.

a) Estimate the weekly sales for the typical McPablo’s outlet?

b) What is the own-price elasticity for tacos? What is the advertising elasticity?

c) Should McPablo’s raise its taco price? Why or why not?

Capps 1 3. Suppose that the demand and supply curves for a particular commodity are given as follows:

Qd = 80,000 – 4,000P, and Qs = -18,000 + 10,000P.

Qd refers to the quantity demanded, Qs= refers to the quantity supplied, and P corresponds to the price.

a) Find the market equilibrium price (P) and quantity (Q).

b) What is the elasticity of demand and supply at the equilibrium price?

c) When P = $6, does a surplus or shortage exist?

d) What is the magnitude of the surplus or shortage?

Capps 2 4. Suppose that Atlantis, Inc., the manufacturer of a microcomputer chip faces demand and cost equations given by Q = 8.5 - 0.05P and TC = 100 + 38Q. Q corresponds to the number of lots of computer chips produced and P corresponds to the price per lot.

a) Derive the inverse demand function.

b) Derive the revenue function. Express your answer in terms of Q.

c) Derive the profit function. Express your answer in terms of Q.

d) What value of Q maximizes profit for Atlantis, Inc? Provide both first-order and second-order conditions to substantiate your answer.

e) What price should Atlantis, Inc. charge for a particular lot of computer chips to assure profit maximization?

f) What is the maximum level of profit Atlantis, Inc. may earn?

Capps 3 5. Suppose that you gain employment with Chili’s Restaurants as a research analyst. You note that historically Chili’s sells 20,000 fajita entrees among various locations in the Dallas Metroplex when the price per entrée is $10.00. You also realize that the own-price elasticity for fajita entrees is -1.5.

a) Is this own-price elasticity a reasonable estimate of behavior of Chili’s patrons? Why or why not?

b) Suppose that management wishes to lower the price of fajita entrees to $9.00. Provide a prediction of the number of fajita entrees that will be sold at this price. Show all work.

c) Will this action, all other factors invariant, result in a rise or fall in sales revenue?

d) What is the magnitude of the gain or loss in revenue?

Capps 4 6. The demand for Kellogg’s Raisin Bran cereal is given as:

1.4 0.75 0.65 0.12 0.05 QKRB = 0.25PKRB PGMC PKFF I A , where

QKRB denotes the quantity of Kellogg’s Raisin Bran sold, PKRB denotes the price of Kellogg’s

Raisin Bran, PGMC denotes the price of General Mills Cheerios, PKFF represents the price of Kellogg’s Frosted Flakes, I represents U.S. disposable income, and A represents the level of advertising expenditures associated with Kellogg’s Raisin Bran.

a) What is the technical name of this type of demand function?

b) TRUE or FALSE. The demand for Kellogg’s Raisin Bran is elastic.

c) If General Mills raises the price of Cheerios by 4 percent, then the quantity of Kellogg’s Raisin Bran sold rises by ______percent, all other factors invariant. Show all work.

d) Both General Mills Cheerios and Kellogg’s Frosted Flakes are ______for Kellogg’s Raisin Bran.

e) True or False. The chief competitor of Kellogg’s Raisin Bran is Kellogg’s Frosted Flakes. Shed light on your answer.

f) To offset a 5 percent increase in the price of Kellogg’s Raisin Bran, by how much should Kellogg increase their advertising expenditures associated with this cereal? Show all work.

Capps 5 g) What type of good is Kellogg’s Raisin Bran cereal? Shed light on your answer.

h) List two additional factors, besides those that have been given, that would potentially affect the demand for Kellogg’s Raisin Bran.

7. Hirschey, P3.10 (pp 106-107)

Capps 6