Industrial Organization Problem Set 1 Due 11.00 am, February 2, 2015, via Aula Global Christian Michel
The problem set consists consists of three problems. problems. You are encourage encouraged d to work work together, together, ideally in groups up to maximum maximum 4 people. Only one (!) student student per group should should upload the work work online via Aula Global. The others others should should simply simply write the name name of the upload uploader er on Aula Global Global.. Please Please write all names names of the group group members mem bers and the associated associated seminar seminar groups on the Problem Set. In case you have trouble with the online form, form, please please inform inform the class teachers teachers before(!) the assignment assignment deadline.
1. (Cournot [Hint: All necessary information to compute the solution is within the Static Oligopoly Lecture note]) In an industry, there are three firms producing a homogeneous product. They are competing in quantities (i.e. one-shot one-shot Cournot Cournot competition). competition). Let q i denote the output level of firm i (i=1,2,3). (i=1,2,3). The market market demand is gvien by P = 15 − Q, where Q = q 1 + q 2 + q 3 . The cost function function is identical identical between between firms and given by C (q i ) = 6q i . This implies that there are no fixed costs of production. (a) What is the equilibrium quantit quantity y for each each firm? (b) Derive Derive equilibrium equilibrium profits for each each firm, consumer consumer surplus, and total surplus. surplus. (c) No Now w assume assume that firm 2 want wantss to acquire acquire firm 3. After After the merger merger,, they they would would form single single firm have 2 firms left in the industry industry). ). The only M with a cost function C M M (q M M ) = 3q M M (i.e. we only have competitor left in the market is firm 1 with the same cost function as before. i. Derive Derive the equilibrium equilibrium quantities quantities after the merger. merger. ii. Derive Derive new individual individual firm profits, industry profits, profits, and consumer consumer surplus. iii. Would a competition authority that is interested in maximizing consumer surplus approve approve such a merger? Discuss (maximum 2 sentences). iv. What is the minimum minimum price firm 2 would have have to pay to the owner owner of firm 3 so that it agrees to sell his firm? Given Given these costs, would would the acquisition acquisition of firm 3 be profitable for firm 2? Also discuss the economic reasoning behind (maximum 2 sentences). 2. (Hotelling (Hotelling duopoly) duopoly) Consider a linear Hotelling duopoly, where consumers are uniformly distributed over a line of length zero, and two firms A and B are initially located at the ends of the line. A consumer of type x derives utility 1 − tx − p1 if she purchases product A (location 0) and utility 0 .8 − (1− (1 − x)t − p2 if she purchases product B (location (location 1). Suppose that parameter parameter values are such that in the equilibrium equilibrium to be charact characterize erized d below, below, the market is fully covered (You can assume that 0 .25 > t > 0.1). Firms set prices simultaneo simultaneously usly.. [Note: If you prefer, you can compute the equilibrium for t = 0.2 with a slight drop in points instead] (a) Derive Derive
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i. The location of the consumer indifferent between A and B , depending on the prices of the both firms ii. the equilibrium prices and quantities of both firms (hint: given (i), set up the maximization problems first, then derive the reaction functions and solve for the equilibrium prices) iii. equilibrium profits iv. consumer surplus, and welfare (optional) (b) For this subquestion you do not have to derive anything, simply use your own reasoning: Imagine now a regular Hotelling-line without making the linear differentiation cost assumption : There is a beach with consumers of length 1, and consumer demand for icecream is uniformly differentiated on the line, without more assumptions on the differentiation costs being made so far. i. Assume a regulator does not understand game theory, and simply assigned two locations for the stores arbitrarily, the location for firm A at 0 .6, and the location for firm B 0 .8. Will firms always oppose such a behavior by the regulator and lobby for a competitive location outcome? Explain your reasoning (maximum 5 sentences). ii. What should the regulator optimally do if he could intervene in the market with respect to locations and prices? (maximum 3 sentences) (c) Give 2 examples from the real world not discussed in the lecture for which the Hotelling model could be applied, and explain (max 4 sentences for each example) (d) Could you think of some limitations of this model to model real world product differentiation? (max 5 sentences) 3. (Vertical Product Differentiation [Hint: All necessary information to compute the solution is within the product differentiation lecture note]) Consider the model of vertical product differentiation that we discussed in class. That is, consumer i’s indirect utility from consuming good j is given by vij
θ z − p = 0 i j
if i buys good j
j
if she buys nothing
where θ is the individual preference parameter and z j is the vertical quality characteristic. Suppose now, however, that there are four products, and that pairs of z and p are given as follows: (z1 , p1 ) = (5, 5) , (z2 , p2 ) = (3, 1) , ( z3 , p3 ) = (5, 2) , ( z4 , p4 ) = (8, 4) , Assume also that θ is uniformly distributed between 0 and 1, and the total mass of consumers is 1. (a) By looking at the price-quality combinations of each product, can you already rule out a firm from selling a product? State your reasoning. (b) Which product will the consumer with the highest willingness to pay choose, i.e. those with the highest θ values? What would be the second best option these consumers consider? Which consumer type (θ) is indifferent between these two options? (c) Where is the consumer located that is indifferent between buying a product and rather choosing no product at all (which generates 0 utility)? Which product is he considering choosing? 2
(d) Calculate the market share of each good and the “outside option.” (The outside option market share is defined as the share of of the potential consumers who do not end up choosing one of the products 1 − 4, as in (c).
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