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3 Long-run equilibrium with heterogeneous firms (34 points) Consider the market for bicycles. There are two technologies used by firms in this industry: Technology 1 uses solar power, and has a cost function C' (q) = q + 4q2 + 32 for q > 0. Technology 2 uses electricity from the grid and is more efficient, with a cost function (2(q) = q + 2q2 + 32 for q > 0. Assume that we are in the long run, so firms using both technologies can shut down and leave the market at 0 cost, so that C(0) = 0 for both technologies. 2. (5 points) Find the individual supply curve of a firm operating Technology 2. 3. Suppose that market demand for bicycles is given by D(p) = 820 - 40p. (a) (2 points) What will be the long-run price in the market? (b) (1 point) How much will each firm produce at this price? (c) (2 points) What will the total number of firms be? 4. (6 points) Now, suppose that the government offers solar subsidies to 10 bicycle manufacturers. These subsidies are for $28 and the manufacturers receive these subsidies as long as they produce a positive quantity of bikes with the solar technology (i.e. technology 1). What are new AC, MC, and supply curve for the solar technology with the subsidy? 5. (a) (2 points) What will be the long run price now that there are the 10 bicycle manufacturers using technology 1 (assuming that there is still free entry for firms using technology 2)? (b) (2 points) What quantity will be produced by firms using technology 1 and 2? (c) (2 points) In equilibrium, how many firms using technology 2 will there be in the market? 6. (4 points) Will either type of firm make any profit in equilibrium? If so, how much will they make? If your results differ by firm, explain the intuition for why firms using some technologies make profits while others do not. 7. (4 points) Now suppose that the government increases the number of solar bike manufacturing subsidies it will give from 10 to 500. What is the new long-run price? How much will be produced by firms of each type? How many firms will their be of each type? Do any firms make profits