Chapter 10, Problem 42RE

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Profit** Suppose that for a product in a competitive market, the demand function is

Find the maximum profit. *(Hint:* First find the equilibrium price.)

To determine

**To calculate:** The maximum profit if the demand function is *x* is the number of units and *p* is in dollars.

Explanation

**Given Information:**

A firms average cost function for this product is

**Formula Used:**

The total profit function is:

Where

**Calculation:**

Consider the provided equation,

In case of equilibrium, it means that supply is equal to demand.

The cost at equilibrium can be calculated as follow:

Put the values of supply and demand equal:

Solve it further for the value of *x*:

Add

Deduct 200 from both the sides,

Hence, the equilibrium price at

The revenue as mentioned in the question is:

*x* is the quantity.

The cost is:

Hence, the profit function is equal to:

Simplify the equation further,

In order to maximize the profit, the following steps have to followed:

Take out the first derivative of the equation by the power rule,

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