Econ 711 Week #9 Discussion: Competitive Markets and Monopoly Power, Study notes of Microeconomics

Download Econ 711 Week #9 Discussion: Competitive Markets and Monopoly Power and more Study notes Microeconomics in PDF only on Docsity! Econ 711. Discussion. Week #9. 11-03-06 Danqing Hu & Michael Rapp 1 Competitive Markets Exercise 1 (Varian 13.1.) Let v (p) + m be the indirect utility function of a representative consumer, and let  (p) be the pro…t function of a representative …rm. Let welfare as a function of price be given by v (p) +  (p) : Show that the competitive price minimizes this function. Can you explain why the equilibrium price minimizes this welfare measure rather than maximizes it? Exercise 2 (MWG 10.C.6) A tax is to be levied on a commodity bought and sold in a competitive market. Tow possible forms of tax may be used: In one case, a speci…c tax is levied, where an amount t is paid per unit bought or sold; in the other case, an ad valorem tax is levied, where the government collects a tax equal to  times the amount the seller receives from the buyer. Assume that a partial equilibrium approach is valid. 1. Show that, with a speci…c tax, the ultimate cost of the good to consumers and the amounts purchased are independent of whether the consumers or the producers pay the tax. 2. Show that this is not generally true with an ad valorem tax. In this case, which collection method leads to a higher cost to consumers? Are there special cases in which the collection method is irrelevant with an ad valorem tax? 2 Monopoly Power Exercise 3 (MWG 12.B.2) Consider a monopolist with cost function c (q) = cq; with c > 0; facing de- mand function x (p) = p; where  > 0: 1. Show that if   1; then the monopolist’s optimal price is not well de…ned. 2. Assume that  > 1: Derive the monopolist’s optimal price, quantity, and price-cost margin (pm c) =pm: Calculate the resulting deadweight welfare loss. 3. (Harder) Consider a sequence of demand functions that di¤er in their levels of  and but that all involve the same competitive quantity x (c) [i.e., for each level of , is adjusted to keep x (c) the same]. How does the deadweight loss vary with ? 1