Midterm 2 (40 points total) (A) (2 points) Define exogenous barriers to entry. Give an example.


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1 Economics 460 Industrial Organization Your Name Midterm (40 points total) Question 1 (7 points) (A) ( points) Define exogenous barriers to entry. Give an example. Exogenous barriers to entry are barriers which are embedded in the underlying conditions of the market. They are not a choice of the firms. Example: Scale economies, regulatory restrictions (B) ( points) Define endogenous barriers to entry. Give an example. Endogenous barriers to entry are barriers which firms with in the industry can change. They are a choice of the firms. Examples: R&D, Advertising, Excess capacity (C) (3 points) If the market size increases in a given market, what will happen to concentration if there are only exogenous barriers to entry? Justify. Is the situation any different if there are also endogenous barriers to entry? Explain. With many exogenous barriers (sunk costs), as the market size increases the concentration of the industry decreases. This is because the exogenous barriers do not change as the market size increases since they are not a choice of the firms. Thus, all else constant a larger market is able to support more firms which reduces the concentration. With endogenous barriers to entry firms can choose to increase the barriers to entry (R&D, Advertising) as the market size increases to deter entry. This means that concentration does not necessarily decrease as the market size increases. Question (4 points) (A) ( points) What is the principle of maximal differentiation? With price competition, firms avoid the toughness of price competition by differentiating themselves as much as possible relative to each other. (B) ( points) What is the principle of minimal differentiation? In the absence of price competition, firms go where the demand is and end up locating in the same area of the product space. Question 3 (4 points) State whether the following statements are true or false and briefly justify. (Assume a monopolist is producing a single product in the market.) (A) ( points) Firms are always better off under 3rd degree price discrimination than under a uniform price. 1
2 True, firms are always weakly better off under 3rd degree price under uniform price. This is because the firm faces less constraints in its optimization problem. That is, a firm using 3rd degree price discrimination can always choose to charge a uniform price to all the groups if that were optimal. Thus, the firm can do at least as well as uniform pricing and possibly better if charging different prices to each group yields higher profits. (B) ( points) Society is worse off under perfect price discrimination than under a uniform price. False, social surplus is in fact higher under perfect price discrimination than under a uniform price (in a monopoly situation). This is true, despite the fact that the firm captures all potential surplus leaving consumers with none. Society is better off because the sum of consumer and producer surplus is maximized. This occurs because the firm continues to produce products until P i = MC (remember there are as many prices as there are consumers). This eliminates the dead weight loss caused by under production which is usually associated with a monopolist.
3 Question 4 (15 points) Consider a beach that is miles long.,000 people are uniformly spread along the beach. At one end of the beach is firm A selling cold (ie. refrigerated) bottles of water. At the other end of the beach is firm B selling warm (ie. nonrefrigerated) bottles of water. Everyone on the beach prefers cold water to warm water. There is a travel cost to walking along the beach to either of these firms. The utility that individual i located at x i [0, ] obtains from purchasing a bottle of water from firm A is: u ia = 10 p A x i If individual i were to purchase a bottle of water from firm B, their utility would be: u ib = 8 p B ( xi) Assume there are no fixed costs for any of the firms. Marginal cost for firm A is 3 and the marginal cost for firm B is 1. (A) (3 points) Assuming that all consumers will buy a bottle of water from one of these firms, what is the location of the consumer who is indifferent between buying from firm A or firm B? (This location should be a function of the prices of the two firms.) 10 p A x = 8 p B ( x ) x = 1 p A + 1 p B (B) (3 points) What is the demand function for firm A? q A =, 000 x q A = 1, 000( 1 p A + 1 p B) q A =, p A + 500p B (C) (3 point) What is the demand function for firm B? q B =, 000 x q B = 1, 000( ( 1 p A + 1 p B)) q B = 500p A 500p B (D) ( points) Write down the profit functions for each of the two firms. π A = (p A 3)(, p A + 500p B ) π B = (p B 1)(500p A 500p B ) (E) (4 points) Assuming the firms choose prices, solve for the Nash equilibrium prices. 3
4 dπ A dp A = 0 =, 000 1, 000p A + 500p B + 1, 500 p A = p B dπ B dp B = 0 = 500p A 1, 000p B p B = p A p B = ( p B) p B = 3 p A = 5 (F) (3 points)(extra Credit) Compute the matrix of own and crossprice elasticities at these equilibrium prices. Which product is more elastic? How can you tell these two products are substitutes? First need to know equilibrium quantities: Equals: q A =, (5) + 500(3) = 1, 000 q B = 500(5) 500(3) = 1, 000 dq A p A dp A qa dq B p A dp A qb dq A p B dp B qa dq B p B dp B qb Product A (cold water) is more elastic than product B (warm water). The cross price elasticity of the two products are positive, indicating they are substitutes instead of complements. Question 6 (0 points, points for each subquestion) Consider the market for online book sales. For simplicity we shall assume all books sold online are identical (ie. homogeneous goods). The current inverse demand for books online is given by P = Q It is expensive to set up the necessary web site for selling books online and to to build the infrastructure of the company. In fact it costs $1 million, and none of this is recoverable if the firm were to shutdown. The wholesale price of this homogeneous book is $10. And the additional costs incurred by an online book seller in selling a single book to a customer is $5 (shipping and handling costs). (A) Suppose there are N identical firms in this market. Write down the profit function for a single firm in the market for online book sales. π i = P (Q)q i C(q i ) = ( Q)q i (10 + 5)q i = ( (Q i + q i ))q i 15q i (B) Now suppose these N identical firms are involved in Cournot competition. Solve for the bestresponse function of a single firm. dπ i dq i = 0 = Q i 0.01q i 15 q i = 8, Q i 4
5 (C) Determine the Cournot equilibrium level of total output (which will be a function of N). By symmetry, we know q i = q j = q in equilibrium. Hence q = 8, (N 1)q = 8, Nq + 0.5q q = 57,000 (1+N) Q = Nq = 57,000N (1+N) (D) What is the equilibrium level of price (again as a function of N)? P = Q = = N N+1 57,000N (1+N) (E) What is the equilibrium level of profit for an individual firm? ( π i = N N+1 ) 57,000 ( ) 1+N 15 57,000 1+N = N 57,000 N+1 1+N 85 = 57,000 N+1 1+N = 85 57,000 (N+1) (F) Assuming freeentry, how many firms can profitably exist in equilibrium? (You should rounddown, if necessary, to get the largest number of whole firms that can exist without earning negative profits.) Setting π i = 0 and solving for largest number of firms with nonnegative profits can be done either by 1) explicitly solving for N or ) simply by guessing some numbers and doing plug and chug. 1) Explicitly solving: 0 = 85 57,000 (N+1) 1, 000, 000(N + 1) = 85 57, 000 (N + 1) = N + 1 = 4.03 N = 3.03 At most 3 firms could exist in the market. ) Or since π i (N = 3) > 0; π i (N = 4) < 0, it follows that the number of firms that will enter the market is given by: N = 3 5
6 (G) What is the value of the Herfindahl index for this industry in equilibrium with the number of firms you calculated above? H = 3 i=1 s i = 3( 1 3 ) = 0.33 (H) (Extra Credit) If we assume instead that all firms collude, what is the equilibrium level of profit for a single firm as a function of N. Under collusion, no matter how many firms, the equilibrium will have the monopoly level of price and output. The firms then equally divide the monopoly output among themselves. We first solve for the monopoly price and total output: π m = ( Q)Q 15Q dπ m dq = 0 = Q 15 Q = 8, 500 P = (8, 500) = Each firm will produce output equal to Q/N = 8, 500/N and obtain profit equal to π i = P q i C(q i ) = ( N ) N = 4,061,50 N (I) (Extra Credit) If firms are free to enter and join the collusive arrangement, how many firms can profitably exist in equilibrium? π i = 0 = 4,061,50 N = N = 4 6
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