Chapter 11, Problem 37RE

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Taxes** Suppose the supply and demand functions for a product are

*p* is in dollars and *q* is the number of units. Find the tax *t* that maximizes the tax revenue *T* and find the maximum tax revenue.

To determine

**To calculate:** The tax per item that will maximize the total tax revenue if the demand function for a fixed period of time is given by

Explanation

**Given Information:**

The provided expression is demand function for a fixed period of time is given by

Where *t* is the tax per unit.

The total tax *T* is equal to *t* is the tax per unit and *q* is the number of units.

The tax revenue is maximized by finding the value of the variable at first derivative is equal to 0. Also checking by verifying that

**Formula Used:**

The following procedure are used to maximizing total tax revenue,

Step-1 Write the supply function after taxation,

Step-2 Equate the demand function and new supply function to get number of units and tax.

Step-3 Calculate the total revue function

Step-4 Calculate the derivative of revenue function and set equal to zero and solve.

Step-5 Calculate second derivative test to verify the result.

**Calculation:**

The provided expression is

After the taxation, the supply function is equal to

Put the new supply(after taxation) equal to the demand.

Solve to equation further to get the value of *t,*

Add

Deduct *t* from both the sides,

Multiply by *-1* on both the sides,

Then, compute the total tax by the formula

Tax is maximized as follows:

The first derivative of

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