2. Consider a market that consists of 10 consumers, i = 1, ..., 10, each with the following quasi-linear utility functionUi = m; + 48 Vx;over the numeraire good m (whose price is normalized to one) and x; units of good l. There arealso 40 perfectly competitive firms, j = 1, .., 40, that produce good l. Each firm j producesq; units of good l, which are sold at price p, using c; (q;) = q/3 units of the numeraire good.Consumers are price takers, are endowed with wi units of the numeraire.Cj(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.6.(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.(e) Write down the equilibrium utilities u as a function of the initial endowments.

Number of consumers = 10 Individual Utility function : ui = m + 48 (xi)1/3 Value of individual…

2. Consider a market that consists of 10 consumers, i = 1,..., 10, each with the following quasi- linear utility function Uj = M¡ + 48 Vx; over the numeraire good m (whose price is normalized to one) and x; units of good l. There are also 40 perfectly competitive firms, j = 1, ..., 40, that produce good l. Each firm j produces q; units of good l, which are sold at price p, using c; (q;) = q³/3 units of the numeraire good. Consumers are price takers, are endowed with wi units of the numeraire. (a) Derive the individual demand function, x; (p), and aggregate demand function, x (p), of good 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?

2. Consider a market that consists of 10 consumers, i = 1,..., 10, each with the following quasi- linear utility function Uj = M¡ + 48 Vx; over the numeraire good m (whose price is normalized to one) and x; units of good l. There are also 40 perfectly competitive firms, j = 1, ..., 40, that produce good l. Each firm j produces q; units of good l, which are sold at price p, using c; (q;) = q³/3 units of the numeraire good. Consumers are price takers, are endowed with wi units of the numeraire. (a) Derive the individual demand function, x; (p), and aggregate demand function, x (p), of good 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?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter12: The Partial Equilibrium Competitive Model

Section: Chapter Questions

Problem 12.9P

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