Econ 301 Review 1 Spring 2014
1. A consumer can spend her fixed income of $200 on two products, food (F) and luxuries (L). The consumer’s tastes are represented by the utility function U=FL. Food sells for $2 per unit and luxuries sell for $5 per unit.
a) Draw the budget constraint of the consumer and explain your diagram. b) Knowing that the marginal utilities of F and L are MUF = L and MUL = F, respectively, compute the amount of each good in the consumer’s optimal basket.
2. Let income be I = 80, Px = 4, Py = 1, and utility U = xy (with marginal utility MUx = y and MUy = x).
a) Compute the optimal consumption bundle for the consumer.
b) Now, let the price of x fall to 1 and the income fall to 50. Otherwise, there is no change. Is the old bundle still affordable? In what way has “purchasing power” changed, if at all? Is the old bundle optimal? Illustrate the change on a graph.
c) Now, suppose that the price of x falls to 1, but income does not change. What is the new optimal consumption bundle? Illustrate the change on a graph. 3. A consumer’s utility function is U(x,y) = x1/4y3/4, where x is the quantity of good x consumed and y is the quantity of good y consumed. The prices of the two goods are px and py, and the marginal utilities of the goods are MUx = (1/4)x-3/4y3/4 and MUy = (3/4)x1/4y-1/4. a) Derive the consumer’s demand for good x.
b) Discuss the concept of elasticity, with reference to the demand you derived in (a), and contrasting linear and constant elasticity demands.
4. You have been asked to analyze the market for steel. From public sources, you are able to find that last year’s price for steel was $20 per ton. At this price, 100 million tons were sold on the world market. From trade association data, you are able to obtain estimates for the own price elasticities of demand and supply on the world market as 0.5 for supply and -0.25 for demand, respectively.
Suppose you know that demand and supply equations in the market are linear....
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