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The market demand function for a good is given by Q = D(p) = 800 −...

The market demand function for a good is given by Q = D(p) = 800 − 50p. For each firm that produces the good the total cost function is TC(Q) = 4Q+ Q^2/2 . Recall that this means that the marginal cost is MC(Q) = 4 + Q. Assume that firms are price takers.

(a) What is the efficient scale of production and the minimum of average cost for each firm? Hint: Graph the average cost curve first.

(b) What is the supply function of each firm?

(c) If there are currently 100 firms producing the good, what is the market supply function? What is the short-run competitive equilibrium in this market with 100 firms? What is the profit of each firm?

(d) What is the long-run competitive equilibrium price and quantity in this market?

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