PART A
1) The demand for a product is given by P=6600-10Q, where Q is the number of the product sold and P is the price. The total cost of production is C(Q)=Q2 and, therefore, marginal cost MC=2Q
a) What is the optimal output, price, and profit for the firm, respectively? [4 marks]
b) Now assume there is a re-organisation in the firm that changes the organisational architecture. The firm is divided into two profit centres. One division, the production division, produces the product at a total cost of C(Q)=Q2 and then transfers it to the sales division that faces the firm’s demand curve. There are no other costs than the transfer price of the product. The sales division is only allowed to source the product in-house. There is asymmetric information and the production division only decides about the transfer price. The sales division decides the quantity it buys from the production division at the transfer price. Show graphically how to determine the transfer price. Explain the economics of transfer pricing. [4 marks]
c) What is the optimal transfer price, from the perspective of the firm? Calculate the transfer price set by the production division in b). Calculate the resulting profits of each division. [2 marks]
2) Answer the following sub-questions using economic theory, the principal agent theory and empirical evidence.
a) Most UK and American CEOs are paid significantly more than the average employee of their firms. Does this fact suggest that CEOs are overpaid? French and German CEOs earn considerably less than US CEOs, does this suggest that US CEOs are overpaid? [3 marks]
b) The firm’s stock market price is uncorrelated with the FTSE100 index. In economic terms, does it make sense to pay the firm’s CEO based on the FTSE100 index? Explain. [3 marks]
c) Taking into account the article by Bebchuk et al “The Wages of Failure”, discuss the advantages and disadvantages of incentive pay and the problems of incentive pay in the case of Bear Stearns and Lehman Brothers. Also discuss reforming incentive pay to deal with the problems unearthed at Bear Stearns and Lehman Brothers. [4 marks]
3) A firm provides a service to its clients. Let P be the price charged for the service. The demand curve for each client is P=20-0.1Q and the cost curve is C(Q)=10+2Q.
a) If the firm charges a single price for the service, what is the optimal price and quantity Q for the service? Compute the profit per customer. [5 marks]
b) Explain two-part tariffs and its applications. If the firm charges a two-part tariff, what is the optimal up-front fee, the price P and quantity Q per customer? What is the profit per customer in this case? Explain. [5 marks]
4)
a) British Airlines estimates the short-run price elasticity of business (in absolute values) fares to be 2 and the long-run elasticity (in absolute values) to be 5. Is ticket demand more elastic in the short-run or long-run? Does this seem reasonable? Explain. [5 marks]
b) You estimate the (absolute value of the) price elasticity of demand at the current price and quantity to be 0.25. Do you maximize revenue or sales at this price? If not, what do you have to do to increase revenues? Explain. [5 marks]
5) Critically evaluate the advice of the ABC consulting group which recommended to your firm,
“That you analyze all the business divisions in your firm. Rank them on growth potential. Sell all the low-growth units and invest the money in the high-growth units. Make sure not to sell the high-growth units.” Explain. [10 marks]
PART B
6) Suppose demand for a monopolist’s product is given by p = 300 − 6q while the monopolist’s marginal cost is given by MC = 3q.
a) What is the profit-maximising quantity of output for this monopolist is? [4 marks]
b) What is the profit-maximising price? [2 marks]
c) A second firm with the same marginal cost enters. Firms engage in Cournot (quantity) competition. What is the equilibrium quantity? [4 marks]
7) Two major supermarkets, Sainsbury’s (S) and Tesco (T), are attempting to determine whether to enter a new market. First, Sainsbury’s must decide whether to enter the market or stay out. Tesco then observes Sainsbury’s action and also decides whether to enter or stay out. The payoffs to each firm (in billions) are: if both Sainsbury’s and Tesco enter, the payoffs are 5 for S and -15 for T. If S enters and T does not, payoffs are 15 for S, and 0 for T. If S does not enter and T does, payoffs are 0 and 15. If both S and T do not enter, then payoffs are 30 and 10 respectively.
a) Draw the game tree. [4 marks]
b) Determine the subgame perfect Nash equilibrium, i.e. the one that satisfies backward induction. [4 marks]
c) What is a first-mover advantage? Does Sainsbury’s have a first-mover advantage in this game? [3 marks]
8) Consider the game below
P 2
left right
P1 up (0, 0) (-2, 2)
down (2, -2) (-6, -6)
a) Find all (pure and mixed) Nash equilibria of this game. [5 marks]
b) Sketch best response functions of both drivers. [5 marks]
9) Consider two ice cream sellers competing at a beach that is 1km long. Ice cream prices are fixed by the ice cream company, but the ice cream sellers can choose their locations. Customers are located uniformly (spread out evenly on the beach) and they like ice cream but do not like walking. The cost of walking every metre is the same (i.e. linear cost).
a) Where will the ice cream stands be located in the Nash equilibrium if the locations are chosen simultaneously? Why? [5 marks]
b) Give a real-world example of third-degree price discrimination and discuss the welfare implications. (About 200 words) [5 marks]
10) Consider a simultaneous game between the USA and Russia, regarding the war in Afghanistan. Each player has two possible strategies, attack or withdraw. The USA will be player 1 (the row player). The payoffs are as follows:
US attacks, Russia withdraws: 7, 0
US attacks, Russia attacks: -1, -4
US withdraws, Russia withdraws: 1 , 0
US withdraws, Russia attacks: 0 , 8
a) Write down the matrix of the game. Calculate a Nash equilibrium? [5 marks]
b) Critically discuss the following statement: “Rationality is never seen in real life, so we should not be assuming it in game theory.” (About 200 words). [5 marks]
Sample Solution
