Chapter 13.4, Problem 26E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

In Problems 17-26, *p* and C are in dollars and *x* is the number of units.

A monopoly has a total cost function

Find the consumers surplus at the point where the monopoly has maximum profit.

To determine

**To calculate:** The Consumer’s Surplus where the monopoly has maximum profit for a product whose demand function is approximated by

Explanation

**Given Information:**

Demand function is approximated by

Monopoly has cost function

**Formula used:**

According to the Consumer’s Surplus

If the demand curve has equation *x-*axis from 0 to

The Profit Function is:

**Calculation:**

Consider the demand function,

Since, to know the point where the profit is maximized that is

Substitute the value of

Thus, the Profit Function is:

Substitute

Differentiate the profit function to get the maxima,

Now solve for *x,*

And

Differentiate the profit function

The value of this function at

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