Department of Agricultural Economics Oral Capps, Jr

Department of Agricultural Economics Oral Capps, Jr.

Texas A&M University AGEC 317, Fall 2010

Problem Set #3

1.  Aquarius Products, Inc, has just completed development of a new line of skin-care products. Preliminary market research indicates two feasible marketing strategies: (1) creating general consumer acceptance through media advertising or (2) creating distributor acceptance through intensive personal selling. Sales estimates associated with each marketing alternative are as follows:

Media Advertising Strategy Personal Selling Strategy

Probability / Sales ($) / Probability / Sales ($)
0.1 / 500,000 / 0.3 / 1,000,000
0.4 / 1,500,000 / 0.4 / 1,500,000
0.4 / 2,500,000 / 0.3 / 2,000,000
0.1 / 3,500,000

(a) Assume that the company has a 50 percent profit margin on sales (i.e., profits equal one-half of sales revenue). Calculate expected profits for each strategy.

(b) Calculate the standard deviation of the profit distribution associated with each strategy. Which strategy appears to be riskier?

(c) Calculate the coefficient of variation of the profit distribution associated with each strategy. In terms of minimizing relative risk, which strategy should Aquarius Products, Inc. pursue?

(d) Assume that management’s utility function resembles the one illustrated in the following figure. Calculate expected utility for each strategy. Which strategy should the marketing manager recommend?

2. Mimi’s is a chain of gourmet restaurants. The company has a limited amount of capital for expansion and must carefully weigh available alternatives. Currently, the company is considering opening restaurants in Las Vegas, Nevada, or Dallas, Texas. Projections for these two potential outlets under two possible scenarios (A and B), their contributions to profit and probabilities follow:

Which is the more attractive location if we are decision-makers who:

(a)  Seek to maximize the expected value of profit?

(b)  Seek to minimize absolute risk?

(c)  Seek to minimize the relative risk?

(d)  Suppose that the utility function for the CEO of Mimi’s is given by U = , where ∏ corresponds to profit.

(i)  Which location is more desirable if the decision rule is to maximize expected utility?

(ii)  What is the risk premium associated with opening this restaurant in Las Vegas?

(e)  Suppose that the utility function for the CEO of Mimi’s is given by U = , where ∏ corresponds to profit.

(i)  Which location is more desirable if the decision rule is to maximize expected utility?

(ii)  What is the risk premium associated with opening this restaurant in Las Vegas?

3.  Tex-Mex, Inc., is a rapidly growing chain of Mexican food restaurants. The company has a limited amount of capital for expansion and must carefully weigh available alternatives. Currently, the company is considering opening restaurants in Santa Fe or Albuquerque, New Mexico. Projections for these two potential outlets are as follows. Each restaurant would require a capital expenditure of $700,000, plus land acquisition costs of $500,000 for Albuquerque and $1 million for Santa Fe. The company uses the 10% yield on risk-less U.S. Treasury bills to calculate the risk-free annual opportunity cost of investment capital.

City / Outcome /

Annual profit contribution

/ Probability
Albuquerque / Failure / $100,000 / 0.6
Albuquerque / Success / $200,000 / 0.4
Santa Fe / Failure / $40,000 / 0.3
Santa Fe / Success / $60,000 / 0.7

(a) Calculate the minimum certainty equivalent adjustment for each restaurant’s cash flows that would justify investment in each outlet.

(b) Assume that the management of Tex-Mex is risk averse and uses the certainty equivalent method in decision-making. Which is the more attractive outlet? Why?

4. Suppose an individual’s utility, U, is a function of his/her income, y. Denote this utility function as U(y). It is known that U(50) = 10, U(100) = 15, and U(150) = 18.

(a)  Does this person have a decreasing, constant, or increasing marginal utility of income?

(b)  What is this person’s attitude toward risk?

5. Suppose that two projects offer the following payoff matrix:

State of Nature / Probability / Project A / Project B
Status quo / 0.6 / $1,000 / $200
Recession / 0.25 / -$300 / $20
Boom / 0.15 / $2,000 / $1,500

(a)  What project should one choose if a maximin decision rule is used?

(b)  What project should one choose is a minimax regret decision rule is used? Your answer must provide the opportunity loss or regret matrix.