ISI question

Posted by komal on Feb 24, 2012; 2:51pm
URL: http://discussion-forum.276.s1.nabble.com/ISI-question-tp7315017.html

Two firms 1 and 2 sell a single, homogeneous, infinitely divisible good in a market. Firm 1 has 40 units to sell and firm 2 has 80 units to sell. Neither firm can produce any more units. There is a demand curve: p = a - q , where q is the total amount placed by the firms in the market. So if  qi is the amount placed by firm ith firm, q = q1 + q2 and p is the price that emerges. a is positive and a measure of market size. It is known that a is either 100 or 200. The value of a is observed by both firms. After they observe the value of a, each firm decides whether or not to destroy a part of its output. This decision is made simultaneously and independently by the firms. Each firm faces a constant per unit cost of destruction equal to 10. Whatever number of units is left over after destruction is sold by the firm in the market.

Show that a firm’s choice about the amount it wishes to destroy is independent of
the amount chosen by the other firm.