Two Plants You are the manager of a firm that produces output in two plants. The demand for your firm's product is P = 78 - 15Q, where Q = Q1 + Q2. The total costs associated with producing in the two plants are C1 (Q1) = 20 + 1.5Q, and C2( Q2) = 10 + 1Q, if Q2 > 0. How much output should be produced in plants 1 and 2 in order to maximize profits? Q1 = Q 2 What is the optmal price if using both plants? Pa = What are their maximum profits using both plants? $ One Plant Suppose the firm has already built plant 1 and the fixed cost of production is sunk. But, plant 2 has not yet been built yet; the fixed cost of production are not sunk. Suppost that they use only plant 1. (This means that Q2 = 0,and C2 (0) = 0.) How much output should they produce? Q1 = What would be the optimal price? Pb = What is their maximum profit if they only use one plant? $ Should they build the second plant? CPerfect Competition In a competitive market, the inverse demand for milk is, PD = 97 - 1.7Q. The inverse supply of milk is, PS = 17 + 6.4Q. What is the equilibrium quantity of milk? What is the equilibrium price of milk? What is the producers' surplus? What is the consumer surplus? What is the dead-weight loss? Market Power Now suppose that the market in the previous question was run by a cartel. The cartel restricts quantity in order to maximize industry profits. In other words, it acts like a monopolist. The inverse demand for milk is still, PD = 97 - 1.7Q. The marginal cost of producing milk for the cartel is, MC(Q) = 17 + 6.4Q. What is the profit-maximizing quantity of milk? What is the profit maximizing price of milk? What is the marginal cost at the profit maximizing quantity? What is maximum producers surplus? What is the consumer surplus? What is the dead-weight loss?(4 points) The following graph summarizes the demand and costs for a firm that operates in a monopolistically competitive market. Cost Curves What is the firms optimal output? What is the tirm's optimal price? What is the firm's maximum profits? \\ What adjustments should the manager be anticipating? A V (3 points) In a monopoly where the marginal cost is $20 and profit maximizing price is $26.6666666666667, the price elasticity of demand is:(4 points) Consider a monopoly where the inverse demand for its product is given by P = 14 - 1.6Q Based on this information, the marginal revenue function is: MR(Q) = What quantity maximizes revenue? Q = What price maximizes revenue? P = What is the elasticity of demand at this quantity? What is the maximimum revenue? $(2 points) You are the manager of a Mom and Pop store that can buy milk from a supplier at $1.10 per gallon. If you believe the elasticity of demand for milk by customers at your store is -3.7, then your profit-maximizing price is: $