1. The demand for bread per day in a village is: QD = 240 - 4P
a) There are many bakeries, each of which has costs given by: TCA = 200 + 0.5q2 (in ¢)
What is the quantity each bakery produces, the market's equilibrium price and quantity, the number of bakeries in operation, and the market's long run supply function?
b) One of the bakeries invents a new process which costs: TCB = 1500 + 5q What happens to price, the market and the firm's quantities, and the number of bakeries?
c) Now the village council issues an annual license to just one firm, which can operate as many bakeries with costs given by TCA as it desires. What is the new price, quantity for the firm and each bakery, and number of bakeries in operation? What is the firm's supply function, and why? What should this license cost?
d) Distinguish between the market structures in each of the cases above; which is best for the consumer? Distinguish between the role of a bakery in each market structure: does it represent just the plant, the plant and the firm, or the plant, the firm, and the industry? [Hint: consider how many bakeries there are in each firm and in the entire industry.]
2. A firm has two plants with cost functions: TCA = qA2 & TCB = 4qB2
It is the only producer of this good in a country with demand for it given by: QD = 104 - 2P
a) If this good cannot be imported or exported, how much will be produced, and how will production be divided between the two plants? What is the price and the firm's profit?
b) Now the good can be exported and sold at a price of $40, but importing is still banned. What is different in the firm's behavior in the foreign versus the domestic market?
How much will the firm produce, how will production be divided between the two plants, and how much will be sold in the two markets? What is the price in the domestic market, and what will be the firm's profit?