3. (7 points) Market demand is Qd "", p E [0, a] (5) 0, p sa a, b > 0. There are n competitive firms in the market. For 2 = 1, ...,n, firm i hires l; units of labor at unit cost w > 0, which yields q; = 219 units of output. Here, a E (0, 1). (a) Suppose that n = 1. i. Find firm 1's supply as a function of p. (1 point) ii. Find the competitive equilibrium (p*, q1) for any a e (0, 1). (1 point) iii. Find the competitive equilibrium (p*, qi) for a - 0.5. (1 point) (b) Suppose that n = 3 and a = 0.5. Suppose further that firm 1 is given a subsidy on production, i.e., for each unit of output produced by firm 1, the government gives s dollars to firm 1. i. For i = 1, 2, 3, find firm i's total cost, TCi (qi). (1 point) ii. Find the competitive equilibrium (p* , qi, q2, q3). (1 point) iii. What is the effect of s on (p* , qi, q2, 93 )? (2 points)