Economics 101 Summer 2012 Answers to Homework 5 Due 6 20 12 Directions The homework will be collected in a box before the lecture Please place your name TA name and section number on top of the homework legibly Make sure you write your name as it appears on your ID so that you can receive the correct grade Late homework will not be accepted so make plans ahead of time Please show your work Good luck Please realize that you are essentially creating your brand when you submit this homework Do you want your homework to convey that you are competent careful professional Or do you want to convey the image that you are careless sloppy and less than professional For the rest of your life you will be creating your brand please think about what you are saying about yourself when you 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 4Q MC 100 2Q 520 4Q 100 2Q Q 70 units of output P 520 2Q 520 2 70 380 per unit of output b Given the above information calculate this single price monopolist s profit Answer Profit TR TC TR P Q 380 per unit 70 units 26 600 TC 100Q Q2 50 100 70 70 70 50 11 950 Profit 14650 c 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 unit d 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 output 1 Profit per unit 380 170 71 209 29 per unit To 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 14650 2 Consider a monopolist described by the following equations Market demand for monopolist s product P 100 Q ATC for monopolist ATC 20 3 10 Q MC for monopolist MC 20 3 5 Q In 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 question you 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 Q 400 13 Q Q 30 8 or approximately 31 units P 100 31 69 b 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 2139 TC 20Q 3 10 Q2 20 31 3 10 31 31 908 3 Profit TR TC 1230 7 c 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 cost curve 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 2367 TC 20 800 13 3 10 800 13 800 13 2367 Profit TR TC 0 2 e 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 Q 500 5Q 100 3Q 400 8Q Q 50 units P 100 50 50 f Calculate the level of profits for the monopoly if it is regulated to produce that quantity where price equals marginal cost Answer Profit TR TC TR 50 50 2500 TC 20 50 3 10 50 50 1750 Profit 2500 1750 750 g 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 Regulation Monopolist regulated with Marginal Cost Regulation Price Quantity Profits Subsidy Needed to Produce Allocatively Efficient Answer Single Price Monopolist Monopolist regulated with Average Cost Regulation 38 5 61 5 0 Monopolist regulated with Marginal Cost Regulation 50 50 750 Price Quantity Profits 69 31 1230 7 3 Subsidy Needed to Produce Allocatively Efficient None None None No P is greater than MC for the last unit produced when the firm produces 31 units No P is less than MC for the last unit produced when the firm produces 61 5 units Yes P is equal to MC for the last unit produced when the firm produces 50 units 3 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 answers so both students realize that revealing their answers will allow them to concentrate more fully on the exam In addition they both realize that if the …