Suppose] A Cmpany is the sole provider of electricity in the various districts of Dubai. To meet the monthly demand for electricity in these districts, which is given by the inverse demand function: P = 1,200 − 4Q, the company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2; where Q = Q1 + Q2. The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1 C2(Q2) = 6,000 + 3Q2 + 5Q22 Calculate the profit maximizing output levels of each factory? What is the profit maximizing level of price? What is the maximum profit?

Suppose] A Cmpany is the sole provider of electricity in the various districts of Dubai. To meet the monthly demand for electricity in these districts, which is given by the inverse demand function: P = 1,200 − 4Q, the company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2; where Q = Q1 + Q2. The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1 C2(Q2) = 6,000 + 3Q2 + 5Q22 Calculate the profit maximizing output levels of each factory? What is the profit maximizing level of price? What is the maximum profit?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 5E

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[Suppose] A Cmpany is the sole provider of electricity in the various districts of Dubai. To meet the monthly demand for electricity in these districts, which is given by the inverse demand function: P = 1,200 − 4Q, the company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2;        where Q = Q1 + Q2.       The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1 C2(Q2) = 6,000 + 3Q2 + 5Q22 What is the MR function? What is the MC function of each facility? What is the MC function of the firm? Calculate the profit maximizing output levels of each factory? What is the profit maximizing level of price? What is the maximum profit?
[Suppose] A Cmpany is the sole provider of electricity in the various districts of Dubai. To meet the monthly demand for electricity in these districts, which is given by the inverse demand function: P = 1,200 − 4Q, the company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2;        where Q = Q1 + Q2.       The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1 C2(Q2) = 6,000 + 3Q2 + 5Q22 Calculate the profit maximizing output levels of each factory?
[Suppose] A Cmpany is the sole provider of electricity in the various districts of Dubai. To meet the monthly demand for electricity in these districts, which is given by the inverse demand function: P = 1,200 − 4Q, the company has set up two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2;        where Q = Q1 + Q2.       The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q1 C2(Q2) = 6,000 + 3Q2 + 5Q22 What is the MR function? What is the MC function of each facility? What is the MC function of the firm?
Your local county's electricity is supplied by two power plants which, due to anti-collusion laws, are forbidden to communicate with each other when deciding what quantity of electricity to generate and how much to charge for it. The price of electricity in the market is given by 340 - 0.03q1 - 0.015q2, where q1 is the amount of electricity sold by generator 1 and q2 is that sold by generator 2. The cost function for generator 1 is 550 + 0.06q1 + 0.0002(q1)^2 The cost function for generator 2 is 600 + 0.04q2 + 0.0004(q2)^2 a) If the two power generators act as a Cournot duopoly, how much electricity will be produced by generator 1? b) How much power will be produced by generator 2? c) What would the market price be?
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Consider a wholesale electricity market with two types of generators: coal plants and natural gas plants. There are 10 generators for each fuel type. Each generator has a capacity of 1,000 MW. Marginal costs vary across generation types: $10 per MWh for coal and $20 per MWh for natural gas. During peak hours, demand is given by Q = 30,000 – 100P (measured in MWh). During semi- peak hours, demand is given by Q = 22,000 – 100P. During off-peak hours, demand is given by Q = 20,000 – 100P. Assume that a day consists of one off-peak hour and either a semi-peak or a peak hour (so a day contains two hours only!). Probabilities of semi-peak vs. peak hours are 50%- 50%. For now, assume that the market is competitive. Calculate the peak, the semi-peak, and the off-peak prices of electricity. What are the expected daily profits for each plant?
HP has developed a new, high-end, high-resolution printer, which can print 40 pages per minute. Its market research identified two target segments of customers: 3,500 large businesses and 6,500 university labs. A large business has a valuation of $900 for the new printer, whereas a university lab has a valuation of $630. HP’s variable cost for the printer is $450/unit; all fixed costs are sunk. Assume that each customer needs at most one new HP printer (i.e., no customer will buy multiple units). (a) Suppose that HP cannot price discriminate the two segments of customers, i.e., it can charge only one price for its printer. What is HP’s optimal price for the new printer? What is its maximum profit? (b) Suppose that HP can install an extra chip in the printer to slow down printing to 15 pages per minute. Such a chip costs HP $20 to make and install for each printer. The slower version of the printer is valued at $700 by a large business customer and $600 by a university lab. With…
Problem # 1 You are the marketing manager of a firm that produces Titanium and sells this metal to two distinct kinds of customers: aircraft producers and golf club manufacturers. Demand for Titanium by these two market segments is quite different, as described by the respective price equations: PA = 10 - QA./600 and PG = 12 - QG./100, where annual quantities are in thousands of pounds and prices are in dollars. Your firm estimates the marginal cost of titanium production at $4 per pound. a) What is the optimal price and quantity for the aircraft segment? b) What is the optimal price and quantity for the golf segment?
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Best Orange Juice Company is located in Oman. The cost function for total orange juice production (x) is given by C(q) = 0.25x2. Their orange juice is demanded only in Muscat (Muscat demand is xm= 100-2Pm) and Salalah (Salalah demand is xs= 100-4Ps). Therefore, the total demand is x=xm+ xs. If the company can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price would it charge in each location?
Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to $50 and a fixed cost of $22,500. You are asked to advise the CEO as to what prices and quantities BMW should set for sales in Europe and in the United States to maximize its profits. The demand for BMWS in each market is given by: QE = 8,000 - 80PE and Qu = 4,000 - 20 Pu, where the subscript E denotes Europe, the subscript U denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only. Support your answers %3D graphically as well. a. If, by an international agreement between Europe and United States, BMW were forced to charge the same price in each market, what would be the quantity sold in each market, the equilibrium price, and the company's profit? b. Suppose now that Europe and United States signed a new trade package under which BMW now can charge different prices across the two markets. What quantity of BMWS should the firm sell in each market, and what…
Shaughnessy Consulting, LLC currently enjoys a patent on software that estimates economic damages for clients involved in personal injury lawsuits. Demand for my software is QD = 287.5 – 12.5P. Creating the software cost me about $985 in development and coding. I can produce a copy of the software for $11 per unit (constant cost). How many copies of the software should I attempt to sell? At what price should I sell it? How much profit would I make? My patent expires in a year, and I know other economic consultants will produce competing software. What quantity and price will result once competing software emerges? How much consumer surplus will my clients (lawyers) gain once the competitors enter? (For measuring consumer surplus, recall that area of a triangle = ½ * base * height.) How much deadweight loss is created by my patent and monopoly in this software?