If the revenue R and demand Q are related by R = Q(50 – 2Q) find the marginal revenue function. What is the marginal revenue when Q = 10?
(Answer. R’ = 50 – 4Q, so when Q = 10, marginal revenue is 10.)
Suppose the total benefit derived from a continuous decisions, Q, is B(Q) = 20Q − 2Q and the 2 total cost from deciding Q is C(Q) = 4Q + 2Q . The marginal benefit (MB) and marginal cost (MC) 2 is the first order derivative of these functions. MB(Q) = 20 − 4Q and MC(Q) = 4 + 4Q . (1) (4 points, 2 each) What is the total benefit when Q=2? Q=10? (2) (4 points, 2 each) What is...
Suppose the total benefit derived from a continuous decisions, Q, is B(Q) = 20Q − 2Q and the 2 total cost from deciding Q is C(Q) = 4Q + 2Q . The marginal benefit (MB) and marginal cost (MC) 2 is the first order derivative of these functions. MB(Q) = 20 − 4Q and MC(Q) = 4 + 4Q . (6) (4 points) What level of Q minimizes total cost?
Scenario: Suppose that the demand is given by: P = 100 – Q Marginal Revenue is MR = 100 – 2Q and Total Cost function is : TC(Q) = 20Q Assume the firm is a price-maker (monopolist). What is the maximum profit?
Demand: P = 50 - 4Q Supply: P = 2 + 2Q what is the equilibrium price and quantity
The demand function for an oligopolistic market is given by the equation, Q = 275 – 4P, where Q is quantity demanded and P is price (Note: inverse demand for the dominant firm here is P = 50 - .2Q). The industry has one dominant firm whose marginal cost function is: MC = 12 + 0.7QD, and many small firms, with a total supply function: QS = 25 + P. In equilibrium, the total output of all small firms is
8. Consider the following Demand (Price and Marginal Revenue) and Cost (Total and Marginal) relationships expressed as functions of Q: Price = P(Q) = 310 – 2Q TC = TC(Q) = 3500 + 70Q + Q2 MR = MR(Q) = 310 – 4Q MC = MC(Q) = 70 + 2Q a. What is the profit-maximizing level of output? What is the price at that level? b. Should the firm continue operating in the short run? In the long run? c....
Suppose the total benefit derived from a continuous decisions, Q, is B(Q)=20Q-2Q^2 and the total cost from deciding Q is C(Q)=4+2Q^2. The marginal benefit (MB) and marginal cost (MC) is the first order derivative of these functions. MB(Q)=20-4Q and MC(Q)=4+4Q. What level of Q minimizes total cost?
Problem 3: A market with a monopoly producer has inverse demand P = 120 - 2Q (which gives marginal revenue MR = 120 - 4Q). The monopolist has marginal costs are MCQ) = 4Q and no fixed costs. a) What is the monopolist's producer surplus when it charges the profit maximizing uniform price. b) What is the deadweight loss due to monopoly in this market? c) What would the monopolist's producer surplus be if it could engage in first degree...
Given the demand, in dollars, for a certain product is D(q) = 1100 - 2q, where q is the number of items, find the Revenue in terms of price. R(p) = 605000p - 1100p^2 R(p) = 1100p - 2p^2 R(p) = 550p - 0.5p^2 R(p) = 4p^2 - 4400p + 1210000
1. Suppose that demand is given by P=100-Q, marginal revenue is MR=100-2Q, and marginal cost (and average cost) is constant at 20. a. What single price will maximize a monopolist's profit? b. What will be the prices and quantity under two-part pricing? It involves a lump sum fee (e.g., membership fee) equal to the consumer surplus at competitive prices and user fees (i.e., unit price) equal to the competitive price. c. Now the monopolist has another group of consumers whose...