Question

1. Consider a competitive industry with a large number of firms, all of which have identical cost functions c(y) = y^2 + 1. Suppose that initially the demand curve for this industry is given by D(p) = 52 - p: (The output of a firm does not have to be an integer number, but the number of firms does have to be an integer.) Answer part (c) through (e), and please show work?

(c) What will be the equilibrium price? What will be the equilibrium output of each firm? (Hint: in perfect competition market, a typical firm earns 0 economic profit. That is, y* , P=ATC (break even) as well as P=MR=MC. Therefore, at y* , ATC=MC)

(d) What will be the equilibrium number of firms in the industry? What will be the equilibrium output of the industry?

(e) Now suppose that the demand curve shifts to D(p) = 53-p. What will be the equilibrium number of firms? What will be the equilibrium price?

Answer 1

C. As the hint says, at equilibrium, ATC=MC.

Now, the cost function here is given by y²+1. So, MC will be the derivative of this, which is 2y. So MC=2y

Average cost= Total cost/y=(y²+1)/y=y+1/y. Equating MC and Average Cost

y+1/y=2y

Which gives us y=1.

This is the equilibrium output.

At this output, P=MC=2y. Hence, equilibrium price will be 2.

D. The price at this point is 2, which means D(p)=52-2=50. Now of there are n firms in the industry, the supply can be given by

nP/2. Equating this to 50, we get

n*2/2=50. Hence n=50

Since the output of each firm is 1, the industry output is 50.

E. Rest remains same while the demand curve shifts to 53-P. P at equilibrium is still 2 since MC and average costs are still same, we get

D(P)=53-2=51. Again

n*2/2=51, which means number of firms is 51.