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Unformatted text preview: xpense of profit on the other product. 10 m256hw03soln.nb If the firms merge or could somehow get together and collude to set prices higher, they could both make more money.
However, even if they could come to an agreement on higher prices, including how much less firm 1 should charge
than firm 2, as soon as one firm sets its price the other would improve its profit by cutting price. A merger of the firms
would mean that the combined firm would maximize the total profit on the two products instead of trying to maximize
each separate profit on a product at the expense of profit on the other product.
Our assumption is that firms will set price to maximize their own profit. But this has been looking at only their shortrun interests. Even without collusion, firms might realize that their longrun interests are to limit their price cutting,
foregoing shortrun profits in hopes that both firms setting higher prices will allow both firms to make higher profits.
If one firm cuts price it knows that the other firm is likely to follow suit in the next period and then both firms will
make lower profits. This longrun repeated game is different than the shortrun profit maximizing game. Strategies
for repeated games are much harder to analyze. While it may not capture all features of actual competition, the shortrun profit maximizing model of firm behavior and Nash equilibrium are basic tools for understanding the issues
involved in competition. Exercises
Save a copy of this notebook, complete the exercises, save and email the final version to [email protected]
Due in one week, on Tues. 1/31.
Clear all of the symbols we will be using.
In[1]:= Clear p1, p2, q1, q2, a11, a12, a21, a22, b1, b2, mc1, mc2, profit1, profit2 ; As above, suppose the demands for products are 1 and 2 are linear functions given by
In[2]:= q1 p1_, p2_ : a11
q2 p1_, p2_ : a21 p1
p1 a12
a22 p2
p2 b1;
b2; 1. At times x, y, and z, we observe the prices and demand for products 1 and 2, obtaining the
following (...
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This note was uploaded on 07/12/2013 for the course MATH 256 taught by Professor Schantz during the Spring '11 term at Vanderbilt.
 Spring '11
 Schantz
 Math

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