1) Price discrimination and bundling
We consider two regions A and B. Each market has the similar size (i.e. number of consumers) but differs in the willingness to pay for one unit of the good proposed by the firm. On market is a consumer has a unit-demand for the good and her willingness to pay is equal to Bi with i = A,B and with BA > BB. The firm incurs no cost.
1. The monopoly has perfect and verifiable information on consumer characteristics (location and willingness to pay) and therefore is able to price discriminate.
Determine the optimal prices set by the monopoly in both regions. Is this pricing policy robust to arbitrage if there is no transport cost between both regions?
2. What is the optimal price without price discrimination?
Suppose now that BA < 2BB. Furthermore, the firm might propose to consumers a service in addition to the good. The valuation for that service is equal to σ in both regions. The transport cost of the service is infinite.
3. If the monopoly decides to price discriminate, find out the price for each product in both regions. Is that pricing policy robust to arbitrage? The monopoly introduces tie-in sales so that each consumer is now constrained to buy the bundle "good plus service".
4. Find out the price of each bundle if the monopoly price discriminates. Demonstrate that the discriminatory pricing policy is robust to arbitrage if and only if σ < BA−BB. Explain this result.
2) Discriminatory pricing and the investment in personal data
The purpose is to assess the incentive to acquire information on consumer characteristics. We consider a monopoly. The firm incurs no production cost. There are M consumers with unit demand. Consumers’ valuation for that good, denoted v, is uniformly distributed on the interval [0, 1]. A consumer with a valuation v buys the good if and only if the price for the good p is lower than v (p ≤ v). The firm a priori does not observe the valuation v. But the monopoly has the possibility to obtain information, that will lead to a partition of the consumers into N subintervals of equal length. For instance if N = 2, the monopoly knows whether a consumer has a valuation in the interval [0,1/2] or [1/2,/1] and could set two different prices for each sub-group.
1. Find out the optimal price for each sub-group.
2. Deduce the profit of the monopoly. Is there a benefit to invest in information acquisition for the monopoly?
3) "Should we regulate entry?"
We consider N identical firms that compete à la Cournot. Each firm incurs a constant marginal cost c. The demand for the homogenous good is given by the following function: Q = 1 − P where P denotes the unit price of the good.
1. Find out the Nash equilibrium of the Cournot game. Deduce the profit of each firm at the equilibrium. Express the total surplus at the equilibrium. We introduce an entry stage in the game. The game becomes the following:
Stage 1: firms decide simultaneously to enter the market. Entry has a fixed cost F.
Stage 2: the firms compete à la Cournot
2. Find out the free entry number of firms, i.e. the number of firms such that an additional entry would not be profitable (ignore the integer problem).
3. Express the total surplus if N firms enter the market at stage 1. Deduce the optimal number of firms. Can we say that at the equilibrium too many firms enter on the market? Explain.
4) Does fluctuating demand facilitate collusion?
We consider two identical firms that produce the same good. The demand for that good is the function D(p) = 1− p where p is the unit price. Firms incur no cost.
The competition game (simultaneous pricing competition) is repeated infinitely. The discount factor is δ.
We consider the following strategy for each firm:
At period t, firm i :
(i) sets the monopoly price if firm 2 sets the monopoly price at all the previous periods.
(ii) sets a price equal to 0 otherwise
1. What is the condition on δ that ensures that setting the monopoly price at each period is an equilibrium of the dynamic game?
We introduce fluctuations in the market demand. At each period the demand is, with equal probability, either 0 or 2(1−p).
2. What is the new condition on δ which makes collusion on the monopoly price stable?