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EC3260

Summer Examinations 2021/22

Industrial Economics 2: Strategy & Planning

Section A: Answer BOTH questions.

1. There are two identical platforms A and B which have zero costs. The platforms simultaneously set access prices pA  and pB .

There are two ‘sides’ of the market who observe the access prices and choose which    platform to join. Side X have types ex ~U[0, 1] and Side Y have types ey ~U[0, 1]. Their utility from an xy match is:

ux  = uy  = a + Fex ey  − p

where a ≥ 0 is the private benefit from matching, F ≥ 0 measures the importance of match quality and p is the price to access the platform.

(a)   Fix some prices pA  and pB  with pB  ≥ pA . Suppose there is an equilibrium where

each agent  i  (either X or Y side) joins platform B if and only their type ei   is at least as high as some threshold level  . (i.e. they join B if and only if ei  ≥ ).

(i)        If agent i from side X joins Platform A then find E[ey |i joins A]. (2 marks) 

(ii)        If agent i from side X joins Platform B then find E[ey |i joins B]. (2 marks)

(iii)       Assume that  is strictly between 0 and 1. Solve for the fraction of types which join each platform. (6 marks)

(b)   Find the Nash equilibrium in prices. (8 marks)

(c)   Discuss how the outcomes of the model may change in the following cases:

(i)        If the importance of matching quality (F) increased. (4 marks)

(ii)        If there was an additional option of matching outside the platforms (for free)

with a type drawn uniformly from [0, 1]. (4 marks)

(iii)        If each platform developed a technology to match each user with an identical

type (i.e., e = 0.6 X types are matched with e = 0.6 Y types). (4 marks)

2.    This question has two parts, please answer both.

Part I

Consider a manufacturer that sells its product to a retailer who resells it to final consumers. The manufacturer’s marginal cost is zero whereas the retailer’s marginal cost is constant at 1 (that is, each unit that it sells increases the retailer’s total costs by 1). The market has 20   consumers of type A and 40 consumers of type B. Each consumer would like to buy at most one unit. A consumer of type A is willing to pay up to $10 and a consumer of type B is           willing to pay up to $5. The manufacturer has the bargaining power to offer a contract to     the retailer. The retailer has an alternative profit of $40 and will agree to the  manufacturer's contract as long as the retailer can earn at least $40.

(a)   Suppose that the manufacturer can only charge a wholesale price (price per-unit),

w. The retailer decides whether to accept or reject the manufacturer’s offer, and  then the retailer decides on the price to final consumers. What is the wholesale    price that the manufacturer offers? What is the price, quantity and the profits of  the manufacturer and the retailer? Is there a “double marginalization” problem in this case? (7 marks)

 (b)  Suppose now that the manufacturer still cannot use two-part-tariff (the manufacturer can only charge