A monopoly seller is able to divide its overall market into two submarkets with the demand functions: P1 = 100 – 91 P2 = 120 – 292 The monopoly produces output in a single plant with the cost function (C): C = 20(q1 + q2) Find the optimal production levels (i.e. which maximize profit) for each market.
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- Suppose a certain city has a monopoly cable-television company. This company has total costs TC = 0.25Q2 + 30Q + 70. (Hint: using calculus, this means MC = 0.5Q+ 30since MC is the derivative of TC with respect to output.) The demand in the community is approximated by the equationQd = 60- P/2(alternatively, you can write the demand equation as Qd = 60–0.5P). Graphically depict the demand curve as well as the marginal cost (MC) curve. If the cable company is free to choose its own pricePm and quantityQm, graphically depictthe monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome. Compute and state the exact monopolist equilibrium pricePm and quantityQm that you depicted graphically.Assume a monopoly has two groups of customers, and each group of customers has different demand for the firm's product. Group A's demand is: Pa = 90 - .1qa where qa is group A's quantity demanded and Pa is the commodity's price in dollars for group A customers. Group B's demand is: Pb = 170 - .2qb where qb is group B's quantity demanded and Pb is the commodity's price in dollars for group B customers. The firm's total cost curve is: TC = 30,000 + .05q2 where TC is the firm's total cost in dollars and q is the total quantity of output produced by the firm. Based upon the above equations, answer the following questions: a. What quantity of the commodity would the firm sell to customers in group B? What price would the firm establish for customers in group B? b. What quantity of the commodity would the firm sell to customers in group A? What price would the firm establish for customers in group A?Suppose a certain city has a monopoly cable-television company. This company has total costs TC = Q2 + 10Q + 75. (Hint: using calculus, this means MC = 2Q + 10 since MC is the derivative of TC with respect to output.) The demand in the community is approximated by the equation Qd = 85 - P/2 (alternatively, you can write the demand equation as Qd = 85 – 0.5P). Graphically depict the demand curve as well as the marginal cost (MC) curve. If the cable company is free to choose its own price Pm and quantity Qm, graphically depict the monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome. Compute and state the exact monopolist equilibrium price Pm and quantity Qm that you depicted graphically.
- Suppose a monopoly firm has an annual demand function of Qd = 20,000 - 250P, annual variable costs of VC = 16Q + 0.002Q2 and marginal cost of MC = 16 + 0.004Q, where Q is the annual quantity of output. In addition, the firm has an avoidable fixed cost of $25,000 per year. If this firm maximizes its profit, what is the value of the consumer surplus in the market?A monopoly is considering selling several units of a homogeneous product as a single package. A typical consumer’s demand for the product is Qd = 50 - 0.25P, and the marginal cost of production is $120. Determine the optimal number of units to put in a package. How much should the firm charge for this package?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.
- A nightclub manager realizes that demand for drinks is more elastic among students, and is trying to determine the optimal pricing schedule. Specififically, he estimates the following average demands: • Under 25: qr= 18 − 5p • Over 25: q = 10 − 2p The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the nightclub $2 each. (a) If the market cannot be segmented, what is the uniform monopoly price? (b) If the nightclub can charge according to whether or not the customer is a student but is limited to linear pricing, what price (per drink) should be set for each group? (c) If the nightclub can set a separate cover charge and price per drink for each group, what two-part pricing schemes should it choose? (d) Now suppose that it is impossible to distinguish between types. If the nightclub lowered drink prices to $2 and still wanted to attract both types of consumers, what cover charge would it set? (e) Suppose that the nightclub again restricts itself…A large firm has two divisions: an upstream division that is a monopoly supplier of an input whose only market is the downstream division that produces the final output. To produce one unit of the final output, the downstream division requires one unit of the input. If the inverse demand for the final output is P = 1,000 − 80Q, would the company’s value be maximized by paying upstream and downstream divisional managers a percentage of their divisional profits?. Suppose you are a manager of a County government project that is meant to provide rent-regulated housing units in low-income settlements. Using your knowledge of equilibrium, advice the Governor whether this policy will be a success. b. A Monopolist producing and supplying cooking gas to Mombasa city faces the demand function. Q = 8800 – 20P. Its cost function is given by TC = 20Q + 0.05Q2. i. Determine the quantity of cooking gas she will produce and the price she will charge to maximize profits and determine her profit. ii. Explain how her profits she will affected if regulators forced her to operate like a perfectly competitive firm. iii. Illustrate and compute dead-weight loss and lost consumer surplus associated with her Monopoly operations.
- A firm is a profit-maximizing monopolist in the market of a patented computer software. As an economic analyst,you observe the following data:a) The monopoly’s price is set at $50 per copy.b) The monopoly’s total revenue is $300,000.c) The monopoly’s marginal cost at the profit-maximizing quantity is at $30 per copy.Based on the observed data, please determine the linear inverse demand function.Fill in the blanks. Suppose the inverse demand function is of the formwhere a, b are both positive constants, determine the value for a: 1 and b: 2 .Hint: a should be an integer, the answer for b should round to four decimal places.A manager of a nightclub realizes that demand for drinks is more elastic among students and is trying to determine the optimal pricing schedule. Specifically, he estimates the following average demand for his customer types: Under 25: qr=18-5p Over 25: q=10-2p The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the club $2 to make. If the manager cannot identify to which group his customers belong, what is the uniform monopoly price? If the manager can identify to which group his customers belong, what price will he charge each group. Assume the manager can only charge a single price to each group. If the manager can charge a separate entry fee and a price per drink for each group, what two-part price will the manager set for reach group. Now suppose that once again it is impossible to identify which group the customers belong. Suppose the manager lowers the price of drinks to equal to marginal cost and still wanted to attract both…Assume that a monopolist sells a product with a total cost function: TC = 1200+0.5Q2. The market demand curve is given by the equation: Q=300-P For what range of output will the firm's revenue be increasing? For this monopolist, the profit-maximizing price is _________, at which it will sell __________ units of output. At this price, the monopoly will earn profit equal to ____________ . If this market were supplied by many firms with the same cost function, how much would be produced? _____________ At what price would it be sold? ______________ Calculate the loss in efficiency in this market due to the monopoly _____________