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Consider a competitive industry with a large number of firms, all of which have the cost...

Consider a competitive industry with a large number of firms, all of which have the cost function c(y) = y 2 + 1 for y > 0 and c(0) = 0. Note that the marginal cost for this cost function is MC = 2y for y > 0. Suppose that initially the demand curve for this industry is given by D(p) = 84 − p. Note that the output of a firm does not have to be an integer number, but that the number of firms has to be an interger.

(a) What is the supply curve of an individual firm? If there are n firms in the industry, what is the industry supply curve?

(b) What is the smallest price at which this product can be sold in the long run?

(c) What is the equilibrium number of firms in the industry?

(d) What is the equilibrium price? What is the output of every firm in the industry?

(e) What is the equilibrium output of the industry?

(f) Now, suppose that the market demand curve shifts to D(p) = 84.5−p. What will be the equilibrium number of firms? What will be the equilibrium price? What will be the output of each firm? What will be the profit of each firm?

(g) Now, suppose that the market demand curve shifts to D(p) = 85 − p. What will be the equilibrium number of firms? What will be the equilibrium price? What will be the output of each firm? What will be the profit of each firm?

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