ECN100A (INTERMEDIATE MICROECONOMICS) PROBLEM SET 2 DUE BEGINNING OF CLASS: FEBRUARY 20, 2020 Question 1: Tim Hortons has the following production function, q = K0.25 L0.25 . (a) Show formally whether this production function has increasing, decreasing, or constant returns to scale. (b) Calculate MPL, MPK, and MRTS LK . (c) If input prices are w = 1 and r = 1, calculate Tim Hortons’ cost function. (d) Suppose the production function changes to q = 2K0.25 L0.25 . What is this an example of? Question 2: In the 1960s, Ed Thorp rented an office at $1600 per month which included the cost of electricity. Ed used the office to run a super computer 24/7 to analyze the casino game of blackjack; the computer used $1900 worth of electricity per month. The alternative to renting the office for the computer was to put it in his garage (where he had to pay his own electricity). What was the (opportunity) cost of renting the office? Question 3: Harold the Historian belongs to a University suffering from extreme cutbacks. His income is normally 100 per month but the University lowers it to only 5. Harold tells his friends about his bad fortune who, in return, suggest Harold quit his job and work at Starbucks where his monthly income would be 10. Harold responds that he normally would agree to take the job at Starbucks since the salary is higher, but he has already spent thousands of hours of time studying history. (a) How would an economist comment on Harold’s thinking? Question 4: Please answer the following miscellaneous questions about production and justify your answers. (a) A firm produces identical outputs at two different plants. If the marginal cost at the first plant exceeds the marginal cost at the second plant, how can the firm reduce costs and maintain the same level of output? (b) True or false? In the long run, a firm always operates at the minimum level of average costs for the optimally sized plant to produce a given amount of output. (c) A firm has a cost function given by C (q) = 10q2 + 1000. What is its short run supply curve? What is its long run supply curve? (d) If the supply curves of firm 1 and firm 2 are, respectively, S1 = p − 10 and S2 = p − 15, at what price does the industry supply curve have a kink in it? Question 5: Marcus the Masseuse works variable hours every month depending on interest from clients and the prices he is able to negotiate with them. Unfortunately for Marcus, he suffers from 1 arthritis so the more patients he sees in a month, the more pain he feels in his hands on a given day, and he always wonders whether he is better off driving for Uber (which does not hurt his hands). (a) Which of the following cost functions is consistent with the description above: (a) C (q) = 4q + 15 or (b) C (q) = 4q2 + 20q? (b) Using the cost function you chose above, find Marcus’ long run supply curve for massages: the supply curve tells you for any given price how many massages Marcus would be willing to supply. (c) Plot the supply function, labeling key points. (d) Suppose the government decides to require masseuses to pay a monthly license fee of 100 for the right to sell massages. Solve and plot Marcus’ new long run supply function. Question 6: Suppose in the short run that a price-taking, perfectly competitive firm (Firm A) is currently producing 8 units of a good. The market price is currently 22 and the firm’s marginal cost function is given by MC (q) = 4 + 3q. For all of the questions below, if you do not think you have enough information to answer, state what information you would need to answer the question. (a) Is Firm A’s behavior consistent with profit-maximization? (b) Suppose Firm B operates in the same market and has the same cost function as Firm A but chooses to produce 6 units of output instead of 8. Is Firm B’s behavior consistent with profit-maximization? (c) Do you expect Firm B to continue operating in this industry, or exiting? 2
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