CAS EC536


Economics of Organization


Sample Midterm Exam — Sketched Answers

The exam is worth 50 points. Answer all questions. Be concise, and think before you write. Point values in brackets.


    1. [10] In most restaurants, the waiters receive a large portion of their compensation through tips from customers. Generally the size of the tip is decided by the customer. However, many restaurants require a 18 percent tip for parties of eight or more. Discuss (a) why the practice of tipping has emerged as a major method of compensating the wait staff, (b) why the customer typically decides on the amount of the tip, and (c) why restaurants require tips from large parties.

    a. Tipping provides incentives for waiters to do a better job compared to paying them a straight salary. Tipping provides incentives to provide high quality service and to sell products (since the tip is based on a percentage of the bill).

    b. The customer has the specific knowledge about whether or not the waiter did a good job.

    c. For tipping to work, the customer must follow through on the implicit promise to tip if the quality of service is good. Individuals in large parties often have incentives to shirk on the tip (free ride). For instance, if each individual agrees to place his share of the bill in a common pool, the amount collected is usually less than the bill plus the normal tip. Hence, large parties are less likely to give reasonable tips unless they are required. Requiring a tip helps to solve this agency problem. The waiter has fewer incentives to provide good service, and may also have reduced incentives to sell products.


    2. 2. [10 points total] Consider the following entry game. The market demand is Q = 10 − p, where p is the price denominated in dollars. 

    a) [3] An Incumbant (I) has a constant marginal production cost of $2 per unit delivered. When alone in the market, he sets price to maximize his profit and sells as many goods as consumers will buy at that price. What price does he choose? What profit does he make? Maximizing (p−2)(10−p) yields p = 6 , profit = 16.

    b) [3] A potential rival (E) may enter the market after incurring a fixed cost F > 0. Her marginal cost is also constant at 2. Upon entry, each firm will compete for sales by setting prices, taking the other’s as given. If E doesn’t enter, her profits are 0. Does she enter the market? Does the answer depend on F? As in the problem set, price competition leads to both firms setting p =2: setting p < 2 results in a negative payoff, while if p > 2, the other firm can charge slightly less and gain the whole market. Profit is therefore zero in the pricing subgame, so in any subgame perfect equilibrium, the entrant is better off staying out. The value of F does not affect this answer as long as F > 0.

    c) [4] Player E discovers a new process that will allow her to lower her marginal cost to 0 if she makes a fixed investment R. She would also have to incur the entry cost F if she were to enter the market. Suppose that R+F = $15. Does this alter her decisions about pricing and entry? Explain. Yes. In the pricing subgame, E charges (just less than) 2: as long as she undercuts I’s marginal cost, she gets the whole market and would like to have the highest price possible that still accomplishes this. This yields a profit of just under · 8 = 16, so entry is worthwhile if the total fixed costs R + F are less than 16, as they are here.


    3. [30; 6 for each part] Widgetco, Inc., has two departments, Engineering and Marketing. The managers of each department contributes to widget production. Each can take one of two non-contractible actions. One action, U, makes the widget user friendly; the other, E, makes it elegant. If the managers both managers choose E or both choose U, the widgets will be high-quality and fetch a high price on the market, generating a revenue of 6, which the two divisions split equally. If one chooses E while the other chooses U, however, widgets are low quality and the revenue is only 3, which again is split equally.

    Evidently, from the point of view of revenue maximization, the managers should coordinate on either E or U. The problem is that these managers are both very opinionated about the right way to do business, and because of their differing backgrounds, they disagree on which way that is. Specifically, the engineer suffers a cost of 1 whenever he chooses U, but no cost when he chooses E; the marketer suffers the same cost 1 when he chooses E, but no cost when he chooses U.

    There payoffs can be represented by a one-shot game in normal form as follows:

    For this problem, you may confine attention to pure strategy equilibria.

    a) What quality widgets are produced by the Widgetco? What actions do the managers take?

    high: the (pure strategy) Nash equilibria are UU and EE

    b) Suppose now that due to declining demand for widgets, the revenue for high quality widgets falls to 3 and for low-quality widgets to 1.5. (the cost of not doing things one’s own way remains equal to 1). Thus the new one-shot game is

    The only equilibrium is UE, so low quality is produced.

    c) Suppose that the widgets are produced in an annual production run following the actions taken by the managers. The following year, the man-agers take actions, possibly different from the ones they chose the previous year, and widgets are produced again. If the managers expect that they will continue to be with the firm with probability 0.8, can Widgetco be expected to produce user-friendly widgets every year? Why or why not? What about elegant widgets? Continue to assume the revenue and cost data of part (b) hold in every year. (Hint: compare the payoffs the managers get under these scenarios to the ones they get in part (b).)

    Neither the user friendly nor elegant widgets (UU or EE) are individually rational: for instance UU yields .5 to the Engineer, while in the one-shot equilibrium he would get .75, so would be better off deviating to playing E rather than and getting .75 every period than playing U every period.

    d) The Engineering department manager proposes that they take turns producing high-quality widgets in each style. Specifically, at the beginning of each year, a fair coin will be flipped; if it comes up tails, both managers are to choose U; if heads, they are to choose E. Of course, nothing prevents one manager from deviating from the agreed-upon action once the coin has been flipped, but this can be observed by the other manager.

    If they stick to this agreement, what is the expected annual payoff to each manager? What strategies might they employ to ensure that they do stick to this agreement? Will they be able to sustain high-quality widget production? Why or why not? (Hint: once the outcome of the coin toss is known, only one of the managers is tempted to deviate.)

    Expected payoff per annum is 1. This is sustainable if both managers play grim trigger strategies: consider the Engineer when the coin comes up tails. He gets  if he plays U that period and  if he deviates, so he doesn’t deviate. Similar for the Marketer when the coin comes up heads.

    e) Demand for widgets falls again, so that high-quality widgets generate revenues of only 2.2 and low quality generate 1.1. What do expect will happen now? Why?

    Now the matrix is . Supporting the high-quality equilibrium described in the previous part requires which is not satisfied. thus it is reasonable to expect that only low quality widgets will be produced.