Question

4. Consider an economy with 2 consumption goods and N consumers, all with the same utility function: u(x1, x2) = x ma, 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) = Bg2. 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) = Bo? - q. Solve for the equilibrium price P2. Does this market structure give an efficient equilibrium outcome? Briefly explain the intuition.

Answer 1

hy Demand function PortuTy, income groups Leu + X & Y - 1,2 - 12 x2] & & & & & & & [y. - 24 – P282] x = xx -x -2x = 0 da 2 (4-6) 2, & 2* _ P22 = 0 2 Y. - 22. - P2 de 20 * * *2.20 - 2120 malaysia X22X * * * 827 12x + XL 17. A LA 4 - 2 2 17 17 + P2 x2 yarn (1-12 + 12) y, - 72 (P **** *92) . 72 12 for xe ofy income Similarly, demana denetim group, x12 & 4 2 Totat demand, or + na Nx (4 + 42) cost functim, cer, Pg2 mcz 2ß q 2 P2 Area Bg og at q zo Ave - Are min supply a 7 functim, qz 2015 Peco 20 Total supply, man

at equilibrium, Total supply (x = Total Demand (2) m if mp22 28 && (), +92) P2 z pompy + y2) 12 for ( +92) 1 rooster dom of good 2 beror Pa a price for this case] the demana cuire, P.22 NK (Y, +42) Total Rev. & NA (42) T mox condition, c C) = B & 2 - 2 MR e me o = 2ßq-1 9723 P2 = Nx x 28 (y + 2) 12 - N&B (y , +42) - P2 - The P2' 2 m P2² - T2 > P2 'yir This is wt a efficient equilibrium because in this is because monopoly power of the second cuse. monopolist change higher price at han perfectly competitive market.