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?
Chapter12: The Partial Equilibrium Competitive Model
Section: Chapter Questions
Problem 12.9P
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