Download Lecture Notes on Competitive Markets | ECON 711 and more Study notes Microeconomics in PDF only on Docsity! Econ 711. Discussion. Week #9. 10-31-08 Ignacio Monzón & Ryoji Sawa 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.2 Quasilinear utility) Consider the two-good (numeraire and good l) quasi- linear model with one consumer and one
rm (I = 1; J = 1). The initial endowment of the numeraire is !m > 0, and the initial endowment of good l is 0. Let the consumers quasilinear utility function be (x)+m, where (x) = + lnx for some ( ; ) >> 0. Also, let the
rms cost function be c(q) = q for some scalar > 0. Assume that the consumer receives all the pro
ts of the
rm. Both the
rm and the consumer act as price takers. Normalize the price of good m to equal 1, and denote the price of good l by p. 1. Derive the consumers and the
rms
rst-order conditions. 2. Derive the competitive equilibrium price and output of good l. How do these vary with , , and m? Exercise 3 (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? 1
