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A Monopolistically Competitive Firm Prices Its Product Using the Markup

Question 78

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A monopolistically competitive firm prices its product using the markup pricing formula P = 1.25MC,where MC is the marginal cost of producing an additional unit.Suppose the demand for the firm's product is given by Q = 2000 - 0.1P,so the revenue from selling Q units of the product is PQ = 2000P - 0.1P2.
(a)If the marginal cost of producing each unit of the product is $10,000,calculate the price of the product,the quantity produced,and the firm's revenues,costs,and profits.
(b)Now suppose the marginal cost rises to $11,000.The firm can keep the price of the product unchanged,or it can change the product's price at a total cost of $700,000.Calculate the price,quantity,revenues,costs,and profits as in part (a)both for changing the price and leaving the price unchanged.Should the firm change the price of its product?

Correct Answer:

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(a)P = $12,500,Q = 750,revenues = $9.375...

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