Consider a competitive industry with a large number of firms, all of which have identical cost functions c(y)
= y2 + 1 for y > 0 and c(0) = 0. Suppose that initially the demand curve for this industry is given by D(p) = 52 − p. (A firm's output does not have to be an integer number, but the number of firms does).
a) What is the supply curve of an individual firm? Plot in a graph with output in the x axis and price in the y axis. If there are n firms in the industry, what will be the industry supply curve?
b) What is the smallest price at which the product can be sold without having a loss? Show by plotting the average cost function in the same graph as before.
c) What is the equilibrium number of firms in the industry? (Hint: Take a guess at what the industry price will be and see if it works).
d) What is the equilibrium price? What is the equilibrium output of each firm?
e) What is the equilibrium output of the industry? 2
f) Suppose the demand curve shifts to D(p) = 52.5 − p. What is the equilibrium number of firms? (Hint: Can a new firm enter the market without making a loss?)
g) In equilibrium, what are the price, output and profits of each firm?
Now suppose that the demand curve shifts to D(p) = 53 − p.
h) What is the equilibrium number of firms? What is the equilibrium price?
i) What is the equilibrium output and product of each firm?