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Mathematical Exercises

1. Assume a consumer with the utility function U = U(X, Y) = X2Y2 and the typical budget constraint M = PxX + Py Y
a. Set up the constrained maximization problem and derive the first-order conditions.

b. Derive the consumer’s demand for X and Y in terms of the parameters

From Chapter 6

Technical Problems

2. Fill in the blanks:
a. The price elasticity of demand for a firm’s product is equal to -1.5 over the range of prices being considered by the firm’s manager. If the manager decreases the price of the product by 6 percent, the manager predicts the quantity demanded will ________(increase, decrease) by _______percent.
b. The price elasticity of demand for an industry’s demand curve is equal to -1.5 for the range of prices over which supply increases. If total industry output is expected to increase by 30 percent as a result of the supply increase, managers in this industry should expect the market price of the good to ________(increase, decrease) by ________percent.

6. For each pair of price elasticities, which elasticity (in absolute value) is larger? Why?

a. The price elasticity for carbonated soft drinks or the price elasticity for Coca-Cola.
b. The price elasticity for socks (men’s or women’s) or the price elasticity for business suits (men’s or women’s).
c. The price elasticity for electricity in the short run or the price elasticity for electricity in the long run.