3. (4 p) Consider an economy with 60 identical consumers. Each individual has the same income M = 100 and the

same utility function u(x, y) = y — (10 — x)2. The price of good x is denoted by p and the price of good y is 1. Suppose that good x is produced by identical firms with individual cost function TC(q) = 0,5q2. Assume that there are 90 firms in the industry and new firms can’t enter this industry in the current period. Government

decided to subsidize the production of good x but only 60 out of 90 firms get the subsidy (the firms that get this subsidy are chosen randomly and the result of this choice is announced before the production decision is made).

Subsidy constitutes 50% of the price paid by consumers and it is financed by a lump sum tax (the same for all

consumers). Suppose that entry is still impossible. (a) (1 p) Derive the market demand (do not forget about corner solutions!) (b) (1 p) Suppose that good x is produced by profit-maximising price-taking firms that have the same technology F (K, L) = 4(KL)0'25. The wage rate is 16 and rental rate of capital is 1. Assume that all factors are variable and

derive the individual firm’s supply curve. (c) (0.5 p) Find the resulting equilibrium. (d) (1.5 p) Calculate the resulting gain/loss in total surplus. Comment on the sources of efficiency loss/gain.