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Quiz 20 Monopoly2 ANS

# Quiz 20 Monopoly2 ANS - P and Q in terms of the parameters...

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Shomu Banerjee ECON 201 MONOPOLY WITH TAX QUIZ ANSWERS A monopolist producer faces the (inverse) demand curve given by P = a - Q , where P is the price charged and Q is the quantity demanded. The total cost of producing the good is C ( Q ) = cQ ; the marginal cost is MC = c . (a) Find the price and quantity P * and Q * that maximize the monopolist’s profit in terms of the parameters a and c . Set MR = MC : a 2 Q * = c , so Q * = ( a c )/2. Substitute into the inverse demand function to obtain P * = ( a + c )/2. (b) Suppose the government decides to tax the monopolist's output at a rate of \$ t per unit. Write down the new cost function for the monopoly and find the new profit- maximizing price and output combination,
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Unformatted text preview: P ** and Q **, in terms of the parameters a , c and t . The new cost function is cQ + tQ = ( c + t ) Q , so the new MC is ( c + t ). Setting this equal to the MR , we get a – 2 Q ** = c + t , so Q ** = ( a – c – t )/2. Substitute into the inverse demand function to obtain P ** = ( a + c + t )/2. (c) How much of the \$ t per-unit tax was the monopolist able to pass on to consumers in terms of a higher per-unit price? ( Hint : Take the derivative of the new price P ** with respect to the tax t .) The derivative is dP **/ dt = ½ , so the monopoly was successful in passing only half the tax to consumers in terms of a higher per-unit price....
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