Question #117364

A monopolist demand function is given by; P=Q2-10Q+28 and cost function; C=Q2. If the firm is causing a pollution to the society valued at MC=3, solve for the social optimal level of output and price. What should be the tax level?

Expert's answer

The social optimal quantity is estimated by equating the price to be equal to the marginal cost.

"\\text{P=MC}"

Therefore:

"3=Q^2-10Q+28"

"Q^2-10Q+28-3"

"Q^2-10Q+25"

"\\dfrac {-b \\pm \\sqrt{b^2-4ac}}{2a}"

"\\dfrac {10 \\pm \\sqrt{ (-10)^2-4\\times 1 \\times 25}}{2\\times 1} =5"

The social optimal level is therefore, 5 units.

The optimal price is:

"p=5^2-10\\times 5+28"

"p=3"

Or

"\\text{P=MC}"

"\\text{P=3}"

At social optimum level, there will be no taxation instead the government should instead give subsidies to the monopolist.

Learn more about our help with Assignments: Finance

## Comments

## Leave a comment