A monopoly faces a demand function Q= 3600/p^2 and a cost function C(Q) = 5Q + 80. (a) Find the monopoly’s profit-maximizing output and price. (b) Calculate the monopoly’s profit and producer surplus.
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(a) Find the monopoly’s profit-maximizing output and
(b) Calculate the monopoly’s profit and
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- You own a road resurfacing business called Rockit Asphalting services located in Kingston. You are the only reservicing business in Southern Tasmania. Therefore, you have a local monopoly. Your experience running the company for many years has taught you that market demand for your service can be described by the demand function: p = 20 − q. The cost function is c = q2. Therefore, marginal cost equals 2q. Quantity refers to square metre of road resurfacing. Note the Q denotes aggregate market demand and q denotes your production. Of course, if you are the only supplier than q = Q. Compute profit maximising price and output. Compute profits. The monopoly profit that you have been earning has attracted attention from another firm that will set up operations in Southern Tasmania and compete for market share. You are concerned with losing market share and profit. So, you offer the potential entrant the following deal. Both firms agree to maximise industry profits (joint…A travel agency will plan a group tour for groups of size 35 or larger. If the group contains exactly 35 people, the cost is $280 per person. If each person's cost is reduced by $10 for each additional person above the 35, then the revenue is given by the equation shown below, where x is the number of additional people above 35. R(x) = (35 + x)(280 − 10x) Find the marginal revenue if the group contains 40 people.A natural monopoly is a monopoly that arises because one firm can meet the entire market demand at a lower average _____ cost than two or more firms could. A legal monopoly is a market in which _____ by the granting of a public franchise, government licence, patent, or copyright. A. fixed; competition and entry are restricted B. total; competition and entry are restricted C. variable; profts are maximized D. variable; costs are minimized
- The monthly demand function for a product sold by a monopoly is p = 5900 − 1/2x2 dollars, and the average cost is C = 3090 + 2x dollars. Production is limited to 100 units. a. Find the revenue function R(x). b. Find the cost function, C(x). c. Find the profit function, P(x). d. Find P'(x). e. Find the number of units that maximizes profits. (Round your answer to the nearest whole number.) f. Find the maximum profit. (Round your answer to the nearest cent.)(Prices as signals of quality). Assume that a firm is a monopolist that produces a good of quality θ. The firm knows the quality, the consumers do not. If quality were observable, the firm would face a demand curve Q = θ−P. Quality can be either high (θ = 2) or low (θ = 1). The marginal cost to the firm of producing a low quality good is zero. The marginal cost of producing a high quality good is c > 0. There is no fixed cost. The firm chooses 1 prices as a function of θ. Denote by µ(P) be the probability that consumers assign to the good being high quality given a price P. The demand curve is: Q = 2µ(P) + (1 − µ(P)) − P (i) First find the full information optimal prices and compute profits. (ii) Find a c∗ such that for c>c∗, the full information optimal prices constitute a separating equilibrium. (iii) Assume now that c∗. What is the price that will be chosen by a low quality firm in a…A monopoly is characterized by all of the following except there are only a few sellers each selling a unique product. entry barriers are high. there are no close substitutes to the firm's product. the firm has market power.
- The manager of a local monopoly estimates that the elasticity of demand for its product is equal to -4. The firm’s marginal cost is 25. Express the firm’s marginal revenue as a function of its price then determine the profit-maximizing price.Which of the following statements is TRUE? A) A monopoly cannot set price and quantity such that the point lies above the demand curve. B) A monopoly can charge whatever it wants. C) Profit maximization occurs by setting price first. D) Both A and B. The more inelastic the demand curve, a monopoly A) will have a smaller Lerner Index. B) will face a lower marginal cost. C) will earn less profit. D) will lose fewer sales as it raises its price.An upstream monopoly sells the good x to a downstream monopoly. The downstream monopoly uses this good as an input to produce its output y. The production function of the downstream monopoly is y = x. The downstream monopoly sells its output to final consumers whose aggregate demand curve is y = 12 − p. The upstream monopoly's cost function is c (x)=2x. 1. Find the quantity x the upstream monopoly sells to the downstream monopoly and the quantity y the downstream monopoly sells to the 1 final consumer. Find also the price k the upstream monopoly charges the downstream monopoly and the price p the downstream monopoly charges the final consumers. Compute the profits of each monopoly.
- Consider the following problem: Demand: q = 100-p Retailer: marginal cost of selling r = 10 per unit Manufacturer: marginal cost of producing = 40 per unit Neither firm faces any competitor Suppose now that the retailer and the manufacturer are separate firms. Write down the profit function of the manufacturer if it sells to the retailer at w. You solved for the quantity the manufacturer will sell a minute ago, so you can use that in the profit function, and then you will have a profit function for the manufacturer that does not have p, but only has w in it. Solve for the optimal w for the manufacturer to charge and calculate the quantitysold under that w.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 able to maintain into the long run primarily because a. barriers to entry exist b. of collusive behavior c. of mutual interdependence d. of price taking behavior e. of product differentiation