# Calculus Examples

,

Step 1

Set up the producer surplus where is the equilibrium quantity and is the equilibrium price.

Step 2

Multiply by .

Since is constant with respect to , move out of the integral.

Multiply by .

By the Power Rule, the integral of with respect to is .

Simplify the answer.

Combine and .

Substitute and simplify.

Evaluate at and at .

Simplify.

Raise to the power of .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Raising to any positive power yields .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Add and .

Multiply by .

Subtract from .