Consider the competitive industry for poke, with a large number of firms, all poke restaurants have identical cost functions c (y) = y2 + 1 for y > 0 and c (0) = 0. Suppose that initially the demand curve for the poke 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). Show your work.
What is the supply curve of an individual firm? If there are n firms in the industry, what will be the industry supply curve?
What is the smallest price at which the product can be sold?
What will be the equilibrium number of firms in the industry? (Hint: take a guess at what the industry price will be and see if it works)
What will be the equilibrium price? What will be the equilibrium output of each firm?
What will be the equilibrium output of the industry?
Now suppose that the demand curve shifts to D(p) = 52.5 – p. What will be the equilibrium number of firms?
What will be the equilibrium price? What will be the equilibrium output for each firm? What will be the equilibrium profits of each firm?
