1. Since a firm in monopoly sets its own price, we can write the price as a function of the quantity (the inverse demand function). Write the inverse demand function and interpret the equation you obtain. 2.Using the inverse demand function, write the profit of the firm as a function of q.
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- You are a consultant who is advising a monopoly on the optimal pricing strategy. Your analysis has yielded the following information. • The marginal cost (MC) is $3. • The demand equation is P = 90 - 3Q . The total cost (TC) is given by 35+ 3Q The marginal revenue (MR) is given by 90 - 6Q Based on this information, answer the following questions. Show FULL calculations! (a) Following the concepts of profit maximization, what is the profit maximizing quantity for this monopoly? (b) Following the concepts of profit maximization, what is the profit maximizing price for this monopoly? (c) Following the concepts of profit maximization, what is the monopoly's profit at the profit maximization point?2. Suppose the cost function for a monopoly is given by TC =F+c.q where TC is the total cost, F is the fixed cost and q is the output of the firm. The demand function for the monopoly is given by q = A-bP where A > 0 and b > 0. Find out the profit maximizing price, quantity, and profit for the monopoly. Also find out the expression for the marginal revenue of the monopoly as well as the elasticity of demand facing the monopoly.Suppose a monopoly firm has the following Cost and Demand functions: TC=Q2 P=80-Q MC=2Q MR=80-2Q Carefully explain what the firm is doing and why. Find the firm’s Profit maximizing Q Find the firm’s Profit maximizing P. Find the firm’s Profit. Suppose because of an advertising campaign, which costs $500, the monopoly’s demand curve is: P=100-Q so its MR= 100-2Q. MC=2Q Looking closely at the TC function and the demand curve, explain the effects of the advertising campaign on the equations compared with the equations above in part 1. Find the firm’s Profit maximizing Q Find the firm’s Profit maximizing P. Find the firm’s Profit. Was the advertising campaign successful? Compare 2 w/ 1. Why?
- Draw the graph. If the monopoly is a single price monopoly (usual monopoly, as in chapter 10), then: the monopoly produces a quantity Q = ______ where ________________ (which curves intersect?) the monopoly charges a price of P = ________ the consumer surplus is CS = ______ (identify the area on the graph and calculate it). the producer surplus is PS = _________(identify the area on the graph and calculate it). the deadweight loss of the monopoly (as compared to the perfect competition) is DWL = ______ (identify the area on the graph and calculate it).7. A monopoly firm faces a demand curve given by 2(P) = 40 – 2p. The firm has constant MC=$12. (A) Find the firm's marginal revenue and use this to find the firm's profit-maximizing output and price. Draw a diagram. Hint: first figure out how express the firm's total revenue in terms of Q. Then if you know calculus, take the derivative of this expression with respect to Q to find marginal revenue. If you don't know calculus, recall that for a linear demand curve, (1) the slope of the marginal revenue curve is twice (in absolute value) the slope of the demand curve; and (2) the marginal revenue curve intersects the vertical (price) axis at the same point as the demand curve; and (3) the marginal revenue curve hits the quantity axis at half the distance of the demand curve. (B) Find the price elasticity of demand at the profit-maximizing output and price. Is demand elastic?1. Suppose a firm operates as a monopoly in the domestic (home) market for a product. The demand for itsproduct is given by the inverse demand function: P = 120 −QD. The company’s costs are: T C = 20Q+ 200and MC = $20.A) Find the firm’s profit-maximizing output and price as a monopoly.B) Find the firm’s total profit in the monopoly market.2. Suppose the home country open up to free trade and a foreign competitor enters the market. Assume thatthe foreign firm has the same cost structure as the home firm (the monopoly from the previous question).A) Derive the best response function for each firm (h-home and f-foreign)B) Find each firms’ output, the home market price, and each firms’ profit from the home market3. Now, suppose that in addition to the home country opening up to free trade, the foreign country has alsoopened up to free trade. As a result, both firms sell their product in both markets.A) Find each firms’ overall output, market price in each market, and each firms’ overall…
- Demand function for a monopoly is Q=100- 2P. The firm's cost curve is C(Q)=20+10Q. (show all your answers in a figure too, draw them manually) a. What is the profit-maximizing solution? What is the firms' maximum profit? What is the revenue-maximizing solution? b. What is the Lerner index at profit maximizing quantity? c. Calculate the deadweight loss if the monopoly charges the profit-maximizing price. d. How does charging the monopoly a specific tax for t = $15 per unit affect price and quantity and the welfare of consumers, the monopoly, and society (where society's welfare includes the tax revenue)? What is the incidence of the tax on consumers?Draw the graph. If the monopoly is a single price monopoly (usual monopoly, as in chapter 10), then: the monopoly produces a quantity Q = ______ where ________________ (which curves intersect?) the monopoly charges a price of P = ________ the consumer surplus is CS = ______ (identify the area on the graph and calculate it). the producer surplus is PS = _________ the deadweight loss of the monopoly (as compared to perfect competition) is DWL = ______Suppose the local electrical utility, a legal monopoly based on economies of scale, was split into four firms of equal size, with the idea that eliminating the monopoly would promote competitive pricing of electricity. What do you anticipate would happen to prices?
- Graphically show a monopoly firm that currently sells 250 units of output at a price of $60/unit, where the marginal revenue of the 250th unit is $40, the marginal cost of the 250th unit is $50, and the average total cost at 250 units is $60. [Hint: Based on the information given, is the quantity you’re asked to show the profit-maximizing quantity? Think about what has to be true for profit-maximization.] Based on the graph and assuming the firm attempts to profit maximize (and succeeds), what would happen to price, quantity, MR, MC, and ATC? (rise, fall, or stay the same?)You are the manager of a monopoly, and your demand and cost functions are given by P = 300 − 3Q and C(Q) = 1,500 + 2Q2, respectively. a. What price–quantity combination maximizes your firm’s profits? b. Calculate the maximum profits. c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price–quantity combination? d. What price–quantity combination maximizes revenue? e. Calculate the maximum revenues. f. Is demand elastic, inelastic, or unit elastic at the revenue-maximizing price–quantity combination?Assume that instead of having two firms in the market, we have a monopoly facing the inverse demand P = 400 − 10Q. The monopoly’s marginal cost is $10. Suppose the Monopoly can first degree price discriminate. Find (calculate) the Monopoly’s quantity, price, profit, the consumer surplus and thedeadweight loss in this case. Draw a representative graph here.
