A monopolist faces a demand curve P = 64−2Q and MR = 64−4Q. His marginal cost is MC = 16. (a) Graph the three functions and compute the profit maximizing output and price. (b) Compute the efficient level of output (where MC=demand), and compute the DWL associated with producing the profit maximizing output rather than the efficient output. (c) Suppose the government gave the monopolist a subsidy of $4 per unit produced. The MC would be reduced accordingly to $12 from $16. Compute the profit maximizing output level and the deadweight loss associated with this new output. Explain intuitively why the DWL has changed.

A monopolist with cost function C(q) = ;q? faces 2 consumers with the following demands: p(q1) = 10 - q1 and p(q2) = 20 – 2q2. Determine prices, quantities to be produced and sold and the monopolist's profits in the following cases: (a) The good can be resold at zero cost among consumers and it is technologically impossible to sell it in bundles of more than 1 unit. b) There is resale at zero cost and bundling in packages of arbitrary size. c) Resale is possible at a cost of "t" per unit. d) The good is a personal and non-transferable service. e) Repeat the above analysis, but this time assuming that costs are C(q) = q with q < 8.

Suppose we have a monopolist with the following: D: Q=40-.5P C: TC=50+10Q What is the marginal cost? What is the revenue function? What is the marginal revenue? What is the profit function (as a function of Q)? What quantity maximizes the monopolists profit? What price will the product be sold at? What is the socially efficient quantity? What is the socially efficient price?

Question d, e and f

All 20 consumers are alike and each has a demand curve for a monopolist's product of p=15 -3q. The cost of production C(Q) =2Q. Let the monopolist charge a price of $PM for qM unit purchased. Find the menu prices that maximize profits? (The buyer pays menu price PM for quantity qM) What is the maximum profit the monopolist can earn in this market? (pi)?

Consider a market with 190 consumers. Of these, 90 of them have individual (inverse) demands given by: PM(Q)=10−Q, while each of the other 100 has an individual (inverse) demand of PS(Q)=10−10Q. The cost function of the monopolist serving this market is C(Q) = 6Q - Q^2/400 . (a) Find the aggregate demand. Analyze the cost function and find what kind of returns to scale it exhibits. Compute the efficient total output (ignoring break-even constraints).(b) Compute the optimal linear price (and quantity) for this monopolist, and the deadweight loss.

The demand for good X is given by x = 586 p-6. The good is sold by a monopolist with cost function C(x ) = 4 x and whose is aim is to maximize profit. The firm charges all customers the same price. If the government imposes a per unit tax equal to 4 dollars on the firm, what price will the monopolist charge consumers?

Question 2. A monopolist sells the same product at the same price into two different markets. The demand for the product in market #1 is denoted D₁ (p) = 30 - 2p where p is the unit price. The demand for the product in market #2 is given by D₂ (p) = 80 - 3p. (a) If the monopolist sets a price of $20 per unit, what is the total demand? (b) Explain why elasticity of total demand is not defined at a unit price of $15.

A monopolist faces an inverse demand curve P(q) = 28 – 3q. The cost curve is C(q) = 10q. What is deadweight loss in this market? (a) DWL = 3 (b) DWL = 27/2 (c) DWL = 19 (d) DWL = 27 (e) None of the above.

(a) A monopolist has discovered that the inverse demand function of a person with income Y for the monopolist’s product is P = 0.002Y-Q where P is the price, Y the income, and Q is the output. The monopolist can observe the incomes of its consumers and hence vary its price accordingly. The monopolist has a total cost function C(Q) = 100Q. Calculate the profit maximising price as a function of the consumer’s income Y carefully explaining all the steps in the derivation of the formula.   (b) A monopolist has a constant marginal cost of £2 per unit and no fixed costs. He faces two separate markets in the United States and in the UK. The goods sold in one market are never resold in the other. He sets one price P1 for the US market and another price P2 for the UK market (both measured in £). The demand in the United States is given by Q1=7,000-700P1 and the demand in the UK is given by Q2=1,200-200P1. Calculate the profit maximising output produced and price charged in each country by the…