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To maximize total surplus with a
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- Will a monopoly ever provide a Pareto efficient level of output on its own ?Suppose that Intel has a monopoly in the market for computer chips. In order to produce X computer chips, it costs Intel C(X) = 2X2. (i) Find the marginal cost of producing a computer chip for Intel. ii) The demand for computer chips is X =12 − 0.25P. Find the level of output that maximizes Intel’s profits. What price is Intel charging?Will the monopolist produce an output level that is technically efficient?
- A monopoly produces widgets at a marginal cost of $10 per unit and zero fixed costs. It faces an inverse demand function given by P = 50 - Q. What is the profit under monopoly?A monopolist is deciding how to allocate output between two geographically separated markets. The demand curve for the firm's output in each market is: P1 = 4,000 - 100Q1 P2 = 2,000 - 50Q2 Where P1 and P2 are the prices of the product in each market and Q1 and Q2 are the amounts sold in each market. The firm's marginal cost curve is: MC = 25Q where Q is the firm's entire output (Q = Q1 + Q2) a) how many units should the firm sell in each market? (Keep Q1 and Q2 in decimal form) b) What price should it charge in the first market? (Use Q1 in decimal form) c) What price should it charge in the second market? ( Use Q2 in decimal form)Suppose that a monopolist has a patent for widgets and the demand curve is given by Q(P) = 12 – 0.02P. The monopolist’s total costs are TC(Q) = 25Q^2 + 500. You may assume that widgets are continuously divisible, like corn oil or sand. a: Find the quantity Q* that maximizes the monopolist’s profit by exploiting the marginalcondition, necessary for profit maximization at an interior solution. Neatly show your work.b: Find the price P* that the monopolist charges. Neatly show your work.c: Neatly graph the marginal revenue and marginal cost curves, with Q on the horizontal axis.d: Label relevant areas on your graph using a, b, c, etc. and fill in the following chart.
- Suppose that the demand a monopoly faces is given by: Q = 10 − P + 10A, where Q is the quantity of output and A is the quantity of advertising. Suppose the cost of advertising and output is given by: C(Q, A) = Q^2 + 100A. Derive profit-maximizing quantity, price, and the quantity of advertisingA monopolist has a cost function given by c(y)=y2 and faces a demand curve given by P(y)=120-y. What is the profit maximizing level of output?Which of the following indicates a quantity choice that is allocatively efficient for a monopoly?
- 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. A. 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…Consider a monopoly market in which the market demand curve is given by P = 240 – 2Q, the marginal revenue curve is MR = 240 – 4Q, the marginal cost curve is MC = 2Q, and there are zero fixed costs. Suppose the government intervenes and turns the market into a competitive market, and all the firms in the market have the same marginal cost curve as the monopolist, MC = 2Q, and zero fixed costs. How much is the resulting gain in total surplus?[12:17]800 600 300 400Lynch Enterprises has a monopoly in the production of dehumidifiers. Its factory is located in Spanish Town. There is no other industry in Spanish Town, and the labor supply equation there is W=10+0.1L, where W is the daily wage and L is the number of person-days of work performed. Dehumidifiers are produced with a production function, Q=10L, where L is daily labor supply and Q is daily output. The demand curve for dehumidifiers is P=41−Q/1,000, where P is the price and Q is the number of sales per day. What is the price of dehumidifiers? Select one: a. 31 b. 11 c. 10 d. 100
