SOCS1010: Introduction to Economics I Problem Set 4 Due 6th Dec., 2017 1. Modified version of Nechyba 13.11 and 14.8 Business Taxes. In this exercise, suppose that you have a creative business, in which you are producing online content, using your own labor and some capital (computers and softwares). You are working from your own bedroom, in other words, there was no fixed costs associated with setting up your business. When you work little and then double your working hours and machinery, your output more than doubles. However, when you are already working a lot and have lots of computers running, doubling all your inputs will exhaust you and result in less than doubling your output. In other words, your technology has first increasing but then decreasing returns-to-scale. This technology of producing online content is available to everyone in the world. Assume that your business and the whole industry are operating at the long-run optimum. (a) Graph MC and AC for your own firm. Explain briefly their shapes. Next to your graph, illustrate the (short-run) supply and demand for the industry. Using both graphs, mark the long-run unit price of online content. What is your long-run profit? In each of the following cases, explain what changes for your firm and the industry in the short run and what changes in the long-run. Remember to explain potential changes to MC, AC, demand and supply curves, prices and output levels. (b) The government imposes a flat tax of T on all businesses like yours. (c) Instead of the flat tax, the government imposes a 50% tax on long-run profits from now on. (d) Instead of the above possibilities, the government imposes an \"entertainment tax\" on any online content, charging you t for every unit of online content you sell. 2. Nechyba 14.7 Using License Fees to Make Positive Profit. Suppose you own one of many identical pharmaceutical companies producing a particular drug x. Your production process has decreasing returns to scale but you incur an annually recurring fixed cost F for operating your business. (a) Begin by illustrating your firm's average (long run) cost curve and identify your output level assuming that the output price is such that you make zero long run profit. (b) Next to your graph, illustrate the market demand and (short-run) market supply curves that justify the zero-profit price as an equilibrium price. (c) Next, suppose that the government introduces an annually recurring license fee G for any firm that produces this drug. Assume that your firm remains in the industry. What changes in your firm and in the market in both the short and long run as a result of the introduction of G and assuming that long run profits will again be zero in the new long run equilibrium? (d) Now suppose that G is such that the number of firms required to sustain the zero-profit price in the new long run equilibrium is not an integer. In particular, suppose that we would require 6.5 firms to sustain this price as an equilibrium in the market. Given that fractions of firms cannot exist, how many firms will actually exist in the long run? Hint: Think about what would long-run profit be if 7 firms produced the amount of firm-level output you found in part c. Is that possible? 1/3 (e) What does this imply for the long-run equilibrium price, the long-run production level in your firm (assuming yours is one of the firms that remains in the market), and the long-run profits of your firm? Hint: You must have figured in part d that only 6 firms will remain in industry, however, 6.5 would be needed to produce what you found in part c. Again, start from the (hypothetical) case when 7 firms remain and then think about what happens as the 7th firm exit. How does that affect supply? What happens to price and indsutry output as a result? And finally, what does that imply for your firm's production level and your long-run profits? (f) True or False: Sufficiently large fixed costs may in fact allow identical firms in a competitive industry to make positive long run profits. Hint: This should be straightforward after answering part e. (g) True or False: Sufficiently large license fees can cause a competitive industry to become more concentratedwhere by \"concentrated\" we mean fewer firms competing for each customer. Hint: Again, think back to your answer in parts c (and e). 3. 1% EXTRA CREDIT EXERCISES based on the game we played in class on 22nd Nov., 2017 In this series of exercises, you will actually analyze the transaction data you and your classmates generated in lecture 7 when playing the pit market game. The exercises are worth 1% of your final mark for the module. They are to be completed in Excel and submitted together with the rest of your problem set. For 0.5% of extra credit, you can submit paper-and-pen answers (not using Excel). If doing the exercises in Excel, in your answers, please also include the relevant portion of your Excel worksheet that shows the formulas you used (\"formulas -> show formulas\"). To answer the questions, you will need to refer to the data located on the course's moodle page. For the theoretical questions, use the spreadsheet entitled \"cards\"; for the empirical questions, use the spreadsheet labeled \"transactions\".1 (a) Theoretical Questions i. There were 29 students in the class, but assume for now that there were 28 of you, which we would have divided up to 14 sellers and 14 buyers. We used utility/cost cards as recorded in the Excel file (worksheet \"cards\"). Using these data, draw a graph in Excel of the aggregate supply and demand curves. ii. From the graph you have drawn, indicate the range of competitive prices and the competitive quantity. iii. As I said, there were 29 students in the class, so we were actually unbalanced and had 15 sellers and 14 buyers. For the extra seller, I inserted an extra cost card with 26. Redo parts 1 and 2 in this setting and discuss the difference you find in part 2 compared to the 14 seller + 14 buyer case. iv. As we will discuss in more detail next week, consumer surplus is the sum of (utility - market price) for all buyers; while producer surplus is the sum of (market price - cost) for all sellers. Calculate the consumer surplus and producer surplus, illustrate them in 1 We did not record the partners in transaction. Therefore, where there were multiple transactions at the same price in a round, I paired up sellers and buyers with the same transaction price randomly. 2/3 your graph of the market demand and supply curve. (If necessary, use the midpoint of the competitive price range as the market price.) v. Calculate the social surplus (defined as the sum of consumer surplus and producer surplus) at the competitive equilibrium. Illustrate it in your graph of the market demand and supply curve (b) Empirical Questions i. From the transactions data, calculate the total realized surplus (total profits of sellers and buyers) earned by buyers and sellers in each period. Divide this realized surplus by the maximum theoretical surplus calculated in question 1. This fraction (usually multiplied by 100 to express it as a percentage) is a measure of market efficiency. ii. Calculate the average transaction price and the standard deviation for each of the rounds of the experiment. iii. In Excel, plot the average transaction price and standard deviation series calculated above. Does the standard deviation of the transaction prices has a decreasing trend over time? Why or why not? Explain. 3/3