Need help with part B: A monopoly sells its goods in the U.S. and Japanese markets. The American inverse demand function is: PA = 140-3QA and the Japanese inverse demand function is: PJ = 100-2QJ Assume that the rm's marginal cost of production is m = 50 in both countries. (a) If the firm can price discriminate (prevent resale between markets), what price will it charge, how much will it produce, and how much profit will it earn in each market. (b) Resolve the problem assuming that the firm cannot price discriminate (e.g., pA = pJ = p).
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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.Suppose that a monopolist sells its product in two countries; Japan and Canada. The monopolist’s marginal cost is $60 and total fixed cost is $100. The direct market demand equations in the two countries are as follows:QJ = 200 − 2PJ and QC = 100 − 0.5PC;where the subscript J denotes Japan and the subscript C denotes Canada. Suppose that the monopolist cannot prevent resale, i.e, the monopolist must charge a single price for both countries.a) Derive the direct total market demand equation, QD = f(P).b) What would be the profit-maximizing quantity (Q*), price (P*), and profit (π*)? Please answer both a) and b). Thank you.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.
- 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 monopolist sells two products Q1 and Q2 for which the demand functions are: Q1 = 100 – 3P1 + 2P2 , Q2 = 75+0.5P1 - P2 and the joint cost function is TC = Q1 2 + 2Q1Q2 + Q2 2 . a. Use Cramer’s rule method to find the prices. Solve for the profit maximizing level of output and the maximum profit. b. Use the Hessian to check the second-order condition.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?
- A monopoly sells 30 units of output when price Ksh 12 and 40 units when price is Ksh 10. If its demand schedule is linear, what is the specific form of the actual demand function? Use this function to predict quantity sold when price is Ksh 8. What domain restrictions would you put on this demand function?. 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 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?
- he Pear Computer Company just developed a totally revolutionary new personal computer. Pear estimates that it will take competitors at least two years to produce equivalent products. The demand function for the computer is estimated to be P=2,500−500Q�=2,500−500� where Q� is millions of computers. The marginal (and average variable) cost of producing the computer is $900. Assuming Pear acts as a monopolist in its market, the profit-maximizing price and output levels are per computer and million computers, respectively. The total contribution to profits and fixed costs at this output level is million. Pear Computer is considering an alternative pricing strategy of price skimming. It plans to set the following schedule of prices over the coming two years: Complete the following table by calculating the contribution to profit and overhead for each of the 10 time periods and prices. Time Period Price Quantity Sold Total Contribution ($) (Million)…Suppose a firm can invent a new product. That firm is the only entity in the world that can invent the product. Doing so incurs a research cost of r to be paid once in the first period. The monopoly price for this new product is 6$ per unit and the firm’s production cost after doing the research in (q^2)/2 where q is the quantity of the good produced.Time is discrete and the firm faces the same price and cost function every period. Without a patent, other firms enter the market and those firms can produce the product more efficiently, therefore without a patent, the firm makes zero profit.1) What is the value for the firm of a patent with infinite duration? Assume a discount factor b = 0. 9.2) Suppose that there is no possibility for the firm of keeping a trade secret. The research cost for that good is 30$. The government can create a patent for the good before the firm has to make a research decision. The terms of the patent cannot be changed after its creation. What is the duration…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.