Economics 713: Assignment 5-
Q1. The prices of consumer goods in Los Angeles and Miami are different: some things are cheaper in Miami, while others are cheaper in Los Angeles. Suppose the price of every consumer good in Houston is exactly halfway between the Miami price of that good and the Los Angeles price. A market research firm surveys 1000 consumers, who have different preferences over consumption bundles, and different incomes. The consumers are asked to rank these three cities in terms of the consumption bundles that they could afford in each place. The result of the survey is that 450 consumers rank Los Angeles first, 350 rank Houston first and 200 rank Miami first. Is this consistent with the standard theory of consumer behavior? Prove any claims that you make.
Q2. A firm has a large accumulated inventory of a storable good. There are no competing sellers of this good, and there is a linear relationship between the quantity sold in each period and the price that the firm sets. Inventory holding costs are negligible, but the cost of production is higher than any buyer would ever pay. The firm can borrow and lend freely at a fixed discount rate, and acts to maximize the present discounted value of profits. How will the firm set prices?
Q3. Show from first principles that the Condorcet Paradox is inconsistent with single-peaked preferences.