2021 Midterm 1 - Blank

MEC 470 Industrial Economics Midterm Exam 1 Olin Business School Fall 2021 This is a closed-book exam. You may use notes on one sheet of paper (two-sided and handwritten unless specifically approved otherwise). You cannot share your sheet with other students. Write your answers in the space provided on the exam. If you need additional scrap paper, just ask. Scientific or basic calculators are permitted, but are not necessary. Graphing calculators are not permitted. Please turn off your mobile phones and any other devices. You must work on this exam on your own without consulting with or aiding anyone else. Any violations of Olin’s Integrity Policy or Honor Code will result in a failing grade for the exam, as well as a recommendation of “Fail” to the Honor Code Committee. Show your work and explain your reasoning – you will get substantial partial credit if your reasoning is correct, even if you make a mistake in your calculations. The exam period lasts 80 minutes. Including a short bonus question at the end, the exam is worth 102 points, with point values noted for each question. Remember: the derivative of the function f ( x ) = a + bx + cx 2 is f 0 ( x ) = b + 2 cx . Finally, please read the following statement, and add your ID number below as confirmation that you agree: In accordance with the academic integrity policy of Washington University in St. Louis, and with respect for others in the community, I submit this work for evaluation. I affirm that I have neither given nor received any unauthorized assistance on this work. Student ID Number: Page 1

MEC 470 Industrial Economics Midterm Exam 1 Olin Business School Fall 2021 1. [30 points] Answer the short-answer questions below. (a) [8 points] Suppose you are comparing the concentration of two markets using multiple measures: the C 3 and the Herfindahl index. It turns out that you measure concentration as being higher in market 1 according to the C 3 , but higher in market 2 according to the Herfindahl. State two different things that could be true of market 2 that would cause this discrepancy. (b) [8 points] In the world of fruit-flavored candy, there are two markets: chewy candy and hard candy. The flavors of the products in each market exist on a single spectrum from very sweet to very sour, and consumers in each market are evenly distributed along this spectrum. Suppose it turns out that consumers who buy chewy candy just like the texture and don’t care all that much about flavor, whereas consumers who buy hard candy are very invested in their favorite balance of sweet and sour. Suppose also that new firms can enter either market at any time by choosing an unoccupied location on the flavor spectrum. In which market would you expect to see more products or firms in equilibrium – hard candy or chewy candy? Explain. (c) [14 points] Two competing manufacturers of turbines in Factorytown need workers in order to produce and sell their product. All qualified workers in Factorytown are members of the Turbine Workers Union, and their wages must be negotiated between the manufacturers and the union. A single, uniform hourly wage is negotiated for all workers at both firms. Subject to this wage, the manufacturers attempt to maximize profits by competing a la Cournot. Answer the following. i. [8 points] Suppose the union gets to determine the wage unilaterally (without manufacturer input), that the union’s goal is to maximize total wages earned by turbine workers, and that there is no “cost” to the union of having any particular worker employed at either manufacturer. This bears a striking resemblance to a particular interfirm relationship we have discussed in class. Write which one, and describe in words how you would set up and solve a specific type of model to predict the equilibrium outcome for the manufacturers and the union workers. ii. [6 points] Suppose now that wages have been set at 20 per hour, but the contract is up for renegotiation. One, and only one, of the manufacturers gains access to a new technology that allows it to replace up to 60 percent of its workers with robots that operate at a cost of 15 per hour. Knowing this, the manufacturer relaxes a bit in its negotiations with the union, allowing wages to rise above 20 in the next contract. Assume that all this manufacturer cares about is its own profits, and workers don’t become more productive if they are paid more. What motivation would this manufacturer have to allow wages to rise above the achievable equilibrium even though at least 40 percent of its production must still be done by workers? What advantage could it have to gain? ( Hint: reread the entirety of every part of this question carefully if you are stumped. ) Page 2

MEC 470 Industrial Economics Midterm Exam 1 Olin Business School Fall 2021 2. [34 points] Consider a market in which inverse demand is characterized by the function p = 200 - ( q 1 + q 2 ) . The two firms in this market compete by choosing their quantities of production sequentially; Firm 1 decides on its quantity, then having observed this choice Firm 2 decides on its quantity. Firm 2 has an advantage in terms of its costs: Firm 1’s constant marginal cost is c 1 = 8, while Firm 2’s constant marginal cost is c 2 = 4. However, Firm 1 is not aware of this cost discrepancy. Firm 1 believes that Firm 2’s cost function is identical to its own. Suppose Firm 2 has the opportunity to announce to the world, and thus to Firm 1, its exact cost function before any quantity choices take place (and that if Firm 2 is honest, Firm 1 will believe them). If Firm 2 announces, Firm 1 will know the true c 2 ; if Firm 2 does not announce, Firm 1 will believe c 2 = 8. (a) [12 points] Suppose Firm 2 announces its cost function. Determine Firm 2’s profits, π 2 , in this case. (b) [12 points] Suppose Firm 2 does not announce its cost function. Determine its profits. ( Hint: in this case, Firm 1 expects Firm 2’s costs and response to be different than what they actually are. ) Will Firm 2 announce? (c) [6 points] You also want to determine whether Firm 1 would prefer to know Firm 2’s cost function up front, or act believing Firm 2’s costs are higher than they actually are. Write down the two functions you would compare to make this determination, and plug in the relevant values you have calculated above. Calculate the answer. ( Note: the final calculation is worth only one point, so come back later if you don’t have a calculator. ) (d) [4 points] It turns out, unsurprisingly, that Firm 1 would like to know Firm 2’s actual cost function before acting. Comment briefly on the value of public versus private information, both having and sharing it, in this market game. Are trade secrets always useful? Is it better to know the grim truth or to be obliviously confident? Page 4

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MEC 470 Industrial Economics Midterm Exam 1 Olin Business School Fall 2021 3. [36 points] A new electric car has just been introduced to the market that dispenses candy into your mouth as you drive. The candy is kind of chalky, but the Pezla automobile 1 is still potentially very popular in the St. Louis area. Popular enough, in fact, that two dealerships have sprung up to serve this market: A and B . Demand for the car is strong, but could be stronger if a new model Pezla is demonstrated at the upcoming local auto show. Only one of the dealerships needs to rent space and send a team to the show to enhance demand for the product, though both could do so. The problem is that doing the auto show will be costly for either dealership. Specifically, inverse demand in this market is such that p = 130 - Q + max { s A , s B } × e, where Q is the total quantity of Pezlas, p is the price of a Pezla (in thousands of dollars; you can ignore that though), e is a positive constant, s i = 1 if dealership i chooses to do the auto show while s i = 0 if dealership i chooses not to do the show, and the max { ., . } operator returns the maximum value of the objects inside the brackets. To be clear, this means that max { s A , s B } = 1 if s A = 1, s B = 1, or both, so that as long as at least one dealership does the auto show, demand increases by exactly e , but there is no additional demand growth if both do. Meanwhile, both dealerships have a constant marginal cost of 10 (in thousands of dollars; again you can ignore this), which is just their manufacturer’s wholesale price. However, if either firm chooses to participate in the auto show, they must pay a fixed cost of F . Thus, each dealership’s total cost function can be expressed (for dealer i ), C i ( q i ) = 10 q i + s i F. The two dealerships will first each decide simultaneously whether to participate in the auto show, then (observing what happened at the auto show) compete a la Cournot. You can proceed to solve this game by backward induction. (a) [8 points] Write down the Cournot profits for dealership A as a function of q A , q B , max { s A , s B } , e , and F . Treating all these (except for q A , but including s A because it has already been fixed) as given, derive dealership A ’s best response quantity as a function of the other variables. (b) [4 points] Suppose the dealerships enter the Cournot competition phase of the game with exactly one of them having done the auto show. Explain in one sentence why it does not matter which dealership participated and which did not – their quantities of production in this equilibrium will be the same (that is, q * A = q * B ). (c) [4 points] Use the fact from part (b) to derive the equilibrium output of dealership A , q * A , in terms of max { s A , s B } , and e . (d) [8 points] Given your equilibrium quantities, it can be shown that the equilibrium price in this market is equal to p * = 50 + max { s A , s B } × e 3 (You do not need to show it.) Suppose that e = 30 and F = 1000, and that dealership B does 1 I’m sorry. Honestly. Page 7

MEC 470 Industrial Economics Midterm Exam 1 Olin Business School Fall 2021 not participate in the auto show (that is, s B = 0). Show whether dealership A will want to do the show. (e) [4 points] Suppose instead that dealership B does participate in the auto show. Intuitively (without math), will dealership A want to participate? Why or why not? Given your answer to this part and the previous part, does dealership A have a dominant action? If so, what is it? If not, why not? (f) [8 points] Consider all this from the point of view of the Pezla manufacturer. Why is the dealerships’ equilibrium choice of whether to participate in the auto show a problem for the manufacturer? Name and describe a policy that Pezla could use in order to alleviate this issue. (g) [BONUS: 2 points] Describe in two sentences how you would mathematically incorporate the policy you described in the previous part into the market model. Page 8

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