I31 rr2r3 rr2 rr r2r3c o

The last two parts of this condition are not as easy to interpret economically as the first. Note that had we assumed that the general R^Qi) functions are all concave and the general c(q) function is convex, so that - c(q) is concave, then the profit function—the sum of concave functions—could have been taken to be concave, thereby obviating the need to check the second-order condition.

Example 4 To make the above example more concrete, let us now give a numerical version. Suppose that our monopolistic firm has the specific average-revenue functions

and that the total-cost function is

Then the marginal functions will be r\ = 63 - 80, r'2 = 105 - 10()2 r'3 = 75 - 12q3 c' = 15

When each marginal revenue r\ is set equal to the marginal cost c' of the total output, the equilibrium quantities are found to be e, = 6 q2 = 9 and q3 = 5

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