Question

Please show how to do this

4. Consider an economy with 2 consumption goods and N consumers, all with the same utility function: u(11, 12) = x 22-a, where and a € (0,1). The goods prices are pi = 2 and P2. Among the consumers, half of them each have income yi and the rest have income y2. There are m firms operating in the competitive market for good 2. Each firm has the cost function c(q) = Ba2. First, solve for the equilibrium price P2. Next, given the same group of consumers yet consider an alternative market structure. Suppose the industry of good 2 is monopolistic, with the cost function c(q) = Bq2 – q. Solve for the equilibrium price P2. Does this market structure give an efficient equilibrium outcome? Briefly explain the intuition.

Answer 1

& -Y2 Doc U(X1, X 2) = x, & X2 to N people, Pi=2, & P2. half people income (N12) = y, another Nl2 income for Good 27. in firms, CQ) = ßq2. Now total demand of Good 2 - upp sum of individual demand ♡ (o). Y + Cla) 42 Pe 2- 80+ N (IR) (9,442)

total individual ss of Gooda = Rising segment of MC = 289 80 as perfect compt, 80 _P2 =289 individual ss auwe _QB 80 MRT ss cowe Qs = mas = MP2 at Eqm Qd = QS ♡ Chels (499) = moment (19) (9,1 9 9) B = m INCIA)LY, HY2) B 2 Nm pins

In Monopolistic compt, P = AC. C= 892_q AL= q = Bq - 1. 8o. P2= Bq - 1. 9:= P2+ , Q2 = m (P2+1). 80 at Eqm Q2 = Qad f !) (8,490). B 9 It is not efficient ofc.