Suppose a monopolist has the following cost function C(Q) = 40Q (with marginal cost MC = 40). Suppose it faces market demand of P = 100-½ Q.< (a) Sketch market demand, marginal revenues, and marginal costs. Be neat.< (b) What is the monopolist's optimal level of output, price, and profits? Show your work.< (c) What is the deadweight loss (DWL) associated with the monopoly output? Show your work and explain why the DWL arises.<
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- A monopolist has a cost function given by c(y) = y2 and faces a demand curve given by P(y) = 120 − y. a. What is his profit-maximizing level of output? What price will the monopolist charge? b. Suppose you put a lump sum tax of $100 on this monopolist. What would its output be? c. If you wanted to choose a price ceiling for this monopolist so as to maximize consumer plus producer surplus, what price ceiling should you choose? How much output will the monopolist produce at this price ceiling?A monopolist faces the demand curve Q(P ) = 50 − P 2 . The firm can produce output with marginal costs MC(Q) = Q and no fixed costs. Hint for the following questions: if revenue is of the form R(Q) = (a − bQ)Q, then the derivative of revenue is a − 2bQ. (a) What is the profit maximizing price for the monopolist in this market? (b) What is the deadweight loss from monopoly in this market, compared to the efficient output that sets price equal to marginal cost? *Please fully explain out any mathThe inverse demand function of a monopolist is p(y) = 12 – y, and total costs is C(y)= y2 -20y +10. a. What is the profit-maximizing level of production? b. Suppose the government decides to tax the monopolist so that for each unit the monopolist sells it has to pay a tax of $2. What is the optimal output under this tax? c. Suppose the government now imposes a tax of 10% on the monopolist’s profits. What is the optimal output under this tax?
- A monopolist has a cost function given by C(y)=y2 and faces a demand curve given by P(y) = 120-y. a) What is the profit maximising level of output and the price that the monopolist will charge? Show your calculations. b) If you impose a lump sum tax of £100 on this monopolist, what will be the impact on output? Explain your calculations and the intuition behind your result. c) If you wanted to choose a price ceiling for this monopolist so as to maximise consumer plus producer surplus, what price ceiling should you choose? How much output will the monopolist produce at this price ceiling? Explain your calculations.A monopolist has a demand curve given by P = 90 - 2Q and a total cost curve given by TC = 72 + Q2. The associated marginal cost curve is MC = 2Q, %3D and the associated marginal revenue curve is MR = 90 – 4Q. What is the profit-maximizing quantity and price. How much economic profit does the monopolist earn? Suppose this monopolist could engage in an advertising campaign that would increase demand to P = 108 – 2Q (and MR = 108 – 4Q). What would be the maximum amount this company would be willing to pay for this advertising campaign?1) A monopolist faces a demand curve Q = 600 – 10P and has the total cost curve TC(Q) = 200 + 20Q + 2Q². What is the monopolist's marginal revenue and marginal cost? What is the profit-maximizing price and quantity? What is the maximized profit?
- 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…Market research shows that a particular monopolist faces a market demand function given byIts cost function isP (Q) = 50 - 2Q.C(Q)= 47 + 10Q What is the monopoly market price and quantity? What is the monopolist’s profit? What is consumer surplus at the monopoly price? What would the price and quantity be in this market be if the monopolist behaved as in perfect competition? What is the consumer surplus in the case of perfect competition? Which is higher and why? What is the “social cost” of monopoly?Acme is a monopolist for a good with inverse demand P = 4000 – 6Q, where P is the price in dollars and Q is the amount sold. Acme's variable costs are TVC(Q) = 4Q². With these functions, the marginal revenue is MR(Q) = 4000 – 12Q and marginal cost is MC(Q) = 8Q. a) If Acme has no fixed costs, what is its profit maximizing price? b) If Acme has non-sunk fixed costs of $700,000, is it worth operating or should they shut down?
- A monopolist has a cost function c(q) = 5q+800 and faces aggregate demand q=3000 - 120p. Suppose first that monopolist sells q=400 units. The monopolist's revenue would be The monopolist profit would be The absolute value of the price elasticity of demand would be The consumer surplus would be Now suppose that the monopolist chooses q to maximize its profit. The monopolist's revenue would be The monopolist profit would be The absolute value of the price elasticity of demand would be The consumer surplus would beA monopolist faces a market demand curve given by Q = 70 − P.a. What is the monopolist’s marginal revenue function? [Remember: theconvention is that we write Rev(Q) and MR(Q). I.e., as a function of Q]b. Suppose the total cost is described byTC = 0.5Q^2 − 5Q + 100.What price-quantity combination will be chosen to maximize profits?c. What is the consumer surplus? What is the producer surplus? [For this question,you can decide to count or not count the fixed cost TC(0) of producing nothing. Both arefine.]