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QUESTION 3 Snow Security Services is a monopolist in the market for freeze-resistant wall-top security cameras. The rm has xed costs of 20 and a constant marginal cost of 5 at all levels of output. The demand function for the market is given by D (p) = 12.5 0.25p. (a) Rewrite demand as the inverse demand function. (h) Set up the monopolist's problem and solve for the optimal price and quantity. (c) Calculate the maximized prot for Snowr Security Services. 9 QUESTION 4 Suppose that the inverse demand function for a monopolist's product is p (q) = 9 0.05q while the rm's total cost function is C(q) = 10+ 10g- 4g2 + 3:13. (3) Plot or sketch carefully the demand curve, marginal revenue curve, and marginal cost curve. ([1) At what volume of output does marginal revenue equal marginal cost? (c) What are the prot- maximizing output and price? (Note: you should check the second-order condition to verify that your answer is a maximum). Name: 3. (12 points total) Refer to the table below which contains incomplete short run production and cost data for a firm. The cells you are asked to calculate are shaded and also contain an asterisk (") Labor Output Marginal | Average Total Total Total Average Average Average Marginal Product Product Fixed Variable Cost Fixed Variable Tol Cost of of Cost Cost Cost Cost Cost Labor Labor MP AP TFC TVC TC AFC AVC ATC MC X X 3.00 30.00 X X 10.00 40.00 7.00 2.86 4.29 110.00 4.00 130,00 4.48 Note that you do not have to calculate every number in the table. Just calculate the six numbers asked for In the questions below and any other numbers necessary to perform your calculation. (a) (2 points) For this firm, what is the total cost in the row where the firm hires 1 unit of labor? Show your calculation. (b) (2 points) For this firm, what is the marginal product of the 4th unit of labor? Show your calculation. (c) (2 points) For this firm, what is the average product of labor when 5 units of labor are employed? Show your calculation. (d) (2 points) For this firm, what is the average fixed cost in the row where 3 units of labor are hired? Show your calculation. (e) (2 points) For this firm, what is the marginal cost of each unit of output between 5 and 14 units of output? Show your calculation. (f) (2 points) For this firm, what is the average total cost in the row where 4 units of labor are hired? Show your calculation.duce at constant average = MC = 6, what out put level will the monopolist choose in order to manna a. If the monopolist can pro and marginal costs of AC 13. Assume instead that the monopolist has a cost structure where total costs are described by TC = new2 5Q + 300 and marginal cost is given by MC = 0.5Q 5. With the monopolist facing the same market demand and marginal revenue, what pricequantity combination will be chosen now to maximize prots? What will prots be? c. Assume now that a third cost 5 monopolist's position, with total costs given by TC=.DIQ3 Q2 +45Q+ 100 and marginal costs given by MC = new2 w so + 45. Again, calculate the monopolist's price--::'|go,aritit}r combination that maximizes prots; What will prots be? (Hint: set MC ='MR as usual and use I the quadratic formula or simple factoring the equation for Q.) d. Graph the market demand curve, the MR curve, ' and the three marginal cost curves from part a, part b, and part c. Notice that the monopolist's prot-maldIIg a'oilit)r is constrained by (1) the mar- ket demand curve it faces (along with its associated MR curve), and {2) the cost structure underlying its tructure explains the 11.- production. 1.2-.- \"null-11+ Fl'1.'l'I Hill