21-121 Fall 2000

Assignment 4 Supplementary Problems

In Problems 1 - 3, find the marginal cost and the marginal revenue for the given average cost functions and demand equations.

1. \overline{c} = \frac{10}{q} + 5 + e^{−.1q}

p = 100e^{−.01q}

2. \overline{c} = \frac{100}{q} + \frac{50}{\sqrt{q}} + 2

p = \frac{100}{\sqrt{q}}

3. \overline{c} = \frac{500}{q} + .01q + 10

p = \frac{100}{q + 1}

4. Suppose that the demand for a monopolist’s product is given by p = \frac{200}{q + 1}, where p is the price per unit and q is the number of units, and that the average cost function is given by \overline{c} = 2 + \frac{50}{q}.

(a) Find an expression for the profit P as a function of q.

(b) Find all values of q at which \frac{dP}{dq} = 0.