1. Consider a market that consists of 50 consumers, i = 1, ..., 50, each with the following quasi-linear utility functionUi = mi + log x;over the numeraire good m (whose price is normalized to one) and x; units of good l; and 50perfectly competitive firms, j = 1, ..., 50, that produce good l. Each firm j produces q; unitsof good l using c; (q;) =i's endowment of the numeraire good is wi, i = 1, ...,50.•..q? /2 units of the numeraire good. Consumers are price takers, and(a) Derive the individual demand function, x; (p), and aggregate demand function, x (p), ofgood l.(b) Derive the individual firm supply function, q; (p), and aggregate supply function, q (p),of good l.(c) Find the equilibrium price p* and quantity q* of good l. What is each firm's profit?(d) Find each consumer i's equilibrium consumption of the numeraire m; as a function ofWi. Find the condition on w; that yields a strictly positive solution for m .*(e) Write down the equilibrium utilities u as a function of the initial endowments.

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.. Consider a market that consists of 50 consumers, i = 1, .., 50, each with the following quasi- linear utility function Ui = m¡ + log x;

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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