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# Answer to Question #117364 in Finance for EUCABETH

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?
1
2020-05-21T11:17:41-0400

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.

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