Assume that all firms in a competitive industry have cost curves given by the following: TC = 128 +8q +2q2. Further, the market demand curve is given by: p = 72-2Q. In the long-run market equilibrium, profit for each firm equals:

In a competitive market, firms make zero economic profit in the long run. This is because if firms were making an economic profit, more firms would enter the market, increasing supply and lowering the price until economic profit is zero. Conversely, if firms were making an economic loss, some firms would exit the market, decreasing supply and raising the price until economic profit is zero.

To find the long-run equilibrium price, we first need to find the firm's marginal cost (MC), which is the derivative of the total cost (TC) function with respect to quantity (q). The TC function is given by TC = 128 + 8q + 2q^2. The derivative of this function is MC = 8 + 4q.

In a competitive market, a firm maximizes profit by producing where price equals marginal cost (p = MC). Therefore, we set p equal to MC and solve for q:

72 - 2Q = 8 + 4q

Rearranging terms gives:

2Q = 72 - 8 - 4q 2Q = 64 - 4q Q = 32 - 2q

Since Q is the total quantity supplied by the market and q is the quantity supplied by each firm, Q = Nq, where N is the number of firms in the market. Substituting Nq for Q gives:

Nq = 32 - 2q (N + 2)q = 32 q = 32 / (N + 2)

Substituting q back into the price equation gives the long-run equilibrium price:

p = 72 - 2Q p = 72 - 2Nq p = 72 - 2N(32 / (N + 2)) p = 72 - 64N / (N + 2)

Finally, to find the long-run equilibrium profit for each firm, we subtract total cost from total revenue (TR = pq, TC = 128 + 8q + 2q^2):

Profit = TR - TC Profit = pq - (128 + 8q + 2q^2) Profit = (72 - 64N / (N + 2))q - (128 + 8q + 2q^2) Profit = (72 - 64N / (N + 2))(32 / (N + 2)) - (128 + 8(32 / (N + 2)) + 2(32 / (N + 2))^2)

Simplifying this expression gives the long-run equilibrium profit for each firm. However, as stated at the beginning, in a competitive market, firms make zero economic profit in the long run. Therefore, the long-run equilibrium profit for each firm is zero.