Answer to Question #215659 in Microeconomics for fafa

Question #215659

The demand equation for a company is P = 200 -3x

And the cost function is C(x) = 75 + 80x - x2


a)     Determine the value of x and the corresponding price that maximize the profit

b)     If the government imposes a tax on the company of R4 per unit quantity produced, determine the new price that maximizes the profit.



1
Expert's answer
2021-07-12T12:10:49-0400

a)

The firm makes profit at the point where MR=MC

"profit=TR-TC"

"TR=P\\times Q"

"P = 200 -3x"

"\\therefore TR=(200-3x)x"

"=200x-3x^2"

"MR=200-6x"


"C(x) = 75 + 80x - x^2"

"MC=80-2x"


"MR=MC"

"200-6x=80-2x\\\\200-80=-2x+6x\\\\120=4x\\\\x=30"



b)

After tax, cost increases by 4x

"C(x)=75+80x\u2212x^2+4x\\\\C(x)=75+84x\u2212x^2\\\\MC=84-2x\\\\MC=MRv\\\\84-2x=200-6x\\\\200-84=4x\\\\116=4x\\\\x=29"


"P = 200 -3(29)=113"

Quantity=29 and price=113


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