Example 6.- Let p = a-x, n = 2, C = cx,C = occx. Take t = - c , so
------- 1112 12 ι
A. 2 and 4 hold. It can be easily shown that in the N.E. x* = (a + cc eɪ-
2c^)∕3 and U* = ((a - tɪfɑ - 2)) / 3)2. Thus if α > 2, the output and profits
of firm 1 (which is the most efficient firm) decreases with t.
2
Example 7.- Let p = x + t- A, C = 2.5 x /2, n = 2, with A > t (this implies
--------------------------------- ɪ ɪ
that for x small p is negative but since p is positive in equilibrium the
inverse demand function can be substituted by p = max (O, x + t - A)). Thus,
T=x + t- A- 1.5x so A.4 and the second order condition are fulfilled.
i 1
Then, x = 4(A - t), i.e. x is decreasing on t.
24
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