Exercise 1 Consider a firm operating under perfect competition with the following total cost function C(Q)=Q310Q2+26Q

1. Determine the quantity that the firm would produce under long-run equilibrium conditions. Suppose that the (inverse) demand function of the market is P(Q)=501Q.

2. What is the number n of firms operating in this market in the long run?

3. Assume that, in this sector, production involves the emission of gases harmful to health. Therefore, a tax is introduced, proportional to quantity, at the rate of 10 euros per unit produced, with the stated aim of reducing production and thus harmful emissions. How do the quantity produced and the number of firms vary in the long run? Assume, now, there are n1 firms of TYPE 1 each with cost function C1(Q)=50+50Q+25Q2 and n2 firms of TYPE 2 each with cost function C2(Q)=40+30Q+25Q2

4. Determine the supply function of the industry in the long run.