Question

3. A village has relied on privately owned bakeries to supply the bread it needs. The demand function for bread per day in the village is: D(P) 600 - 5P, where P is the price per loaf of bread. Each bakery's cost function is given by: C()200+q/2 if q>0 but zero if the bakery shuts down. In other words, the fixed cost is not sunk. The bakery sector is competitive. Each bakery takes the price as given a) Derive the marginal and average cost functions for the bakery and graph them. b) Identify the bakery's supply curve on your graph. At what price will the bakery shut down? Explain your answer c Suppose there are 20 bakeries in the village. What is the price of a loaf? How many loaves does each bakery sell and what is its profit? d) Assume there is free entry and exit of bakeries. What do you predict will happen to this market?

Answer 1

D(p) = 600 - SP C(q) = 200 + q^2/2 Marginal cost = mc = dc/dq = 2q/2 = q mc = q Average cost = AC = C/q = 200/q + q/2 when q = 0, AC = infinity when q = 10, AC = 200/10 + 10/2 = 25 when q = 20, AC = 200/20 + 20/2 = 20 mc is 45 degree line as mc = q \r\n we know when q = 0, bakery shutdown because it will not be able to cover variable cost therefore mc = 0 Thus bakery shuts down when price = 0 Industry supply = > nq we know P = mc Q = 20p At equilibrium, supply = demand 20p = 600 - 5p p = 600/25 = 24 Price of loaf = 24 Market quantity of loaves sold = 20(24) = 480 loaf sold by each firm = 480/20 = 24 Each sold by each firm = 480/20 = 24 Each