c. The firms are considering a provision in the acquisition allowing T’s
senior managers (who will continue to work for the combined firm)
to buy back (at a predetermined price) ownership of T in the event
that the firm is found liable. Does such a provision make sense?
Provide a qualitative explanation.- In the quantity-price contract example in Figure 15.2, we noted that the
order quantity, Q 20, is efficient. We can demonstrate that seemingly
reasonable contracting methods can lead to inefficient results: too little
output being produced and sold. As before, let benefits and costs be:
B3Q Q^2 /20 and C Q^2 /40, respectively. Each side knows the
other’s benefit or cost function. The contracting method is as follows:
The seller names a price for its output, and the buyer chooses the
quantity to purchase at this price.
a. Find the buyer’s profit-maximizing purchase quantity as it depends on
the seller’s quoted price P. (Hint:The buyer sets Q to maximize B
B PQ 3Q Q^2 /20 PQ. Treating P as a parameter, set dB/dQ
equal to zero. You should find that P 3 Q/10 or, equivalently,
Q 30 10P.)
b. Find the seller’s optimal price. (Hint:The easiest approach is to use
the price equation, P 3 Q/10, treat Q as the decision variable,
and set MR MC to find optimal quantity and price.)
c. Explain why an inefficient outcome results when the seller quotes a
take-it-or-leave-it price per unit. - Firms A and B are negotiating to conclude a business deal worth
$200,000 in total value to the parties. At issue is how this total value will
be split. Firm A knows B will agree to a 50–50 split, but it also has
thought about claiming a greater share by making a take-it-or-leave-it
offer. Firm A judges that firm B would accept a 45 percent share with
probability .9, a 40 percent share with probability .85, and a 35 percent
share with probability .8. What offer should A make to maximize its
expected profit?
*11. A buyer has value vbfor a potential acquisition and believes the seller’s
reservation price has the cumulative probability distribution F(v). The
buyer chooses P to maximize its expected profit:
Find the buyer’s marginal profit and set it equal to zero. Show that the
buyer’s optimal price satisfies P vbF(P)/f(p), where f(v)
dF(v)/dv is the associated density function. Note that the buyer shades
down its value in making its optimal bid.b(vbP)Pr(P accepted)(vbP)F(P).662 Chapter 15 Bargaining and Negotiation*Starred problems are more challenging.c15BargainingandNegotiation.qxd 9/26/11 11:03 AM Page 662