Economics 101Summer 2012Answers to Homework #5Due 6/20/12Directions: The homework will be collected in a box before the lecture. Please place your name, TAname and section number on top of the homework (legibly). Make sure you write your name as it appearson your ID so that you can receive the correct grade. Late homework will not be accepted so make plansahead of time. Please show your work. Good luck!Please realize that you are essentially creating “your brand” when you submit this homework. Doyou want your homework to convey that you are competent, careful, professional? Or, do you wantto convey the image that you are careless, sloppy, and less than professional. For the rest of yourlife you will be creating your brand: please think about what you are saying about yourself whenyou do any work for someone else!1. Consider a monopolist where the market demand curve for the produce is given by P = 520 – 2Q. This monopolist has marginal costs that can be expressed as MC = 100 + 2Q and total costs that can be expressed as TC = 100Q + Q2 + 50.a. Given the above information, what is this monopolist’s profit maximizing price and output if it charges a single price?Answer:MR = 520 – 4QMC = 100 + 2Q520 – 4Q = 100 + 2QQ = 70 units of outputP = 520 – 2Q = 520 – 2(70) = $380 per unit of outputb. Given the above information, calculate this single price monopolist’s profit.Answer:Profit = TR – TCTR = P*Q = ($380 per unit)(70 units) = $26,600TC = 100Q + Q2 + 50 = 100(70) + (70)(70) + 50 = $11,950Profit = $14650c. At the profit maximizing quantity, what is this monopolist’s average total cost of production (ATC)?Answer:To answer this question we first need to write an expression for ATC.ATC = TC/Q = 100 + Q + (50/Q)Then replace Q with 70 to find the average total cost of producing 70 units of output. ATC= 100 + 70 + (50/70) = $170.71 per unitd. At the profit maximizing quantity, what is the profit per unit for this single price monopolist?Answer:Profit per unit = Price per unit – ATC per unit when producing 70 units of output1Profit per unit = 380 –170.71 = $209.29 per unitTo verify your answer, check that profit per unit times number of units yields the same profit as you got initially. Thus, Profit = (profit per unit)(number of units produced) = ($209.29)(70) = $146502. Consider a monopolist described by the following equations:Market demand for monopolist’s product: P = 100 – QATC for monopolist: ATC = 20 +(3/10) QMC for monopolist: MC = 20 + (3/5)QIn this question we will use the above data to compare a single price monopolist to the same monopolist that is regulated either with average cost regulation or marginal cost regulation. At the end of the questionyou will fill out a table to compare your results. a. Given the above information, what is the profit maximizing price and quantity for the single price monopolist? You should round your answers to the nearest whole number. Answer:To find the profit maximizing quantity for a single price monopolist you want to equate MR to MC. MR = 100 – 2Q. So, 100 – 2Q = 20 + (3/5)Q400/13 = QQ = 30.8 or approximately 31 unitsP = 100 – 31 = $69b. Given the above information, what is the level of profit for this single price monopolist?Answer:To find the firm’s profit you will need to have TR and TC.TR = P*Q = (69)(31) = $2139TC = 20Q + (3/10)Q2 = (20)(31) +(3/10) (31)(31) =908.3Profit = TR – TC = $1230.7c. Suppose this monopolist is regulated to produce at that quantity where price equals average total cost. Calculate the quantity the monopolist will produce and the price it will charge given this regulatory scenario.Answer:To find the quantity where price equals average total cost use the demand curve and the average total costcurve. Hence, 100 – Q = 20 +(3/10) Q or Q = 800/13 units=61.5units. Use the demand curve to find the price associated with 40 units of output. Thus, P = 100 – Q = 100 – 800/13 = $500/13=38.5.d. Calculate the level of profits for the monopoly if it is regulated to produce that quantity where price equals average total cost. Explain how you got your answer. Answer:To find the firm’s profit you will need to have TR and TC. TR = (800/13)(500/13) = $2367TC = (20)(800/13) +(3/10) (800/13)(800/13) = $2367Profit = TR – TC = $02e. Suppose this monopolist is regulated to produce at that quantity where price equals marginal cost. Calculate the quantity the monopolist will produce and the price it will charge given this regulatory scenario.Answer:Use the demand curve and the MC curve to solve for the quantity.100 – Q = 20 + (3/5)Q500 – 5Q = 100 + 3Q400 = 8QQ = 50 unitsP = 100 – 50 = $50f. Calculate the level of profits for the monopoly if it is regulated to produce that quantity where price equals marginal cost. Answer:Profit = TR – TCTR = (50)(50) = $2500TC = (20)(50) +(3/10) (50)(50) = $1750Profit = $2500 - $1750 = $750g. How big a subsidy will the monopoly require in order to be willing to produce at the price and quantity you calculated in part (e)? Explain your answer.Answer:The monopolist will not need to receive a subsidy since when he produces where MR = P in this example he earns a positive profit of $750. Unlike the example in class, this monopolist is not experiencing increasing returns to scale: this is not a natural monopolist. h. Fill in the table below with your findings. Remember that a firm is allocatively efficient if price is equal to marginal cost for the last unit of the good produced by the firm.Single Price Monopolist Monopolist regulated with Average Cost RegulationMonopolist regulated with Marginal Cost RegulationPriceQuantity ProfitsSubsidy Needed to ProduceAllocatively Efficient?Answer:Single Price Monopolist Monopolist regulated with Average Cost RegulationMonopolist regulated with Marginal Cost RegulationPrice $69 $38.5 $50Quantity 31 61.5 50Profits $1230.7 $0 $7503Subsidy Needed to ProduceNone None NoneAllocatively Efficient?No, P is greater than MC for the last unit produced when the firm produces 31 unitsNo, P is less than MC forthe last unit produced when the firm produces 61.5 unitsYes, P is equal to MC forthe last unit produced when the firm produces 50 units3. Consider two students, Jaeho and Lawrence. Both students are taking an exam in their math class this week and they are both, independently, trying to decide whether they will conceal their answers or reveal their answers while working on the exam. It takes time and effort to conceal