PLEASE EXPLAIN THIS SUM STEP BY STEP ON PAPER AND PEN.... [Exclusive Contracts]
Consider a market with an incumbent firm, a potential entrant and a buyer with demand
D(p) = 120 - p:
Suppose the potential entrant is more efficient than the incumbent. The entrant has a unit
production cost of $10 whereas the incumbent has a cost of $20 per unit. However, the entrant
has to pay an entry cost of F = 500. Before entry, the incumbent can propose the buyer to sign
an exclusive contract in exchange of a payment t to the buyer. An exclusive contract prevents the
buyer to purchase from the entrant. The timing is as follows:
1. Incumbent offers buyer exclusive contract with payment t
2. B accepts or rejects
3. E decides to enter or not
4. active firms name price to B
5. B chooses supplier (respecting exclusive contract if in place)
a) Suppose no exclusive contract has been signed. Derive the equilibrium prices, profits and
consumer surplus if (i) the entrant enters and (ii) the entrant does not enter.
b) Give the minimum amount ^t the incumbent has to pay to induce the buyer to accept the
exclusive contract. Give the maximum amount -t the incumbent is willing to pay for an exclusive
contract. Compare ^t and _t and explain the overall outcome of the game.
Suppose now there are two identical buyers with the same demand as above. At stage 1, the
incumbent offers payments t1 and t2 for buyer 1 and buyer 2, respectively, in exchange for an
exclusive contract. At stage 2, the buyers simultaneously decide whether to accept or reject the
offer. Then stages 3-5 follow as above. Note that at stage 4, each active firm is able to name a
different price for each buyer. Finally, suppose that the entry cost of the entrant is now F = 1500.
c) Derive the equilibrium for stages 3-5 as a function of whether (i) both buyers sign exclusive
contracts, (ii) exactly one buyer signs and (iii) no buyer signs.
d) Derive the equilibrium of the buyer acceptance game at stage 2 as a function of the values (t1;
t2).
e) In case there are multiple equilibria in your answer to d), assume that buyers can coordinate
on the Pareto dominant equilibrium. Derive the optimal values for (t1; t2). Do the buyers sign
exclusive contracts in equilibrium? Does entry occur or not? Compare your results to b) and
explain briefly