Question: Consider the cost function C(Q) = 400 + 0.5Q2 for RussCo to produce its new Phone. Using that cost function for the Phone, determine the

Consider the cost function C(Q) = 400 + 0.5Q2 for RussCo to produce its new Phone. Using that cost function for the Phone, determine the profit-maximizing output, price and profit (or loss) for the RussCo Phone, and discuss its long-run implications, under three alternative scenarios: a. RussCo Phone is a perfect substitute with a similar product offered by Apple, Samsung and several other Phones that have similar cost functions and that currently sell for $400 each. b. RussCo Phone has no substitutes and so is a monopolist, and the demand for the RussCo Phone is expected to forever be Q = 69 – (1/5)P . You must show your work. c. RussCo Phone currently has no substitutes, and currently the demand for the RussCo Phone is Q = 88 – (1/5)P, but RussCo anticipates other firms can develop close substitutes in the future. – note you use the earlier listed cost function.

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a RussCo Phone is a perfect substitute with a similar product offered by Apple Samsung and several other phones that have similar cost functions and currently sell for 400 each To determine the profitmaximizing output price and profit or loss for RussCo Phone we need to find the quantity that maximizes profit Profit is calculated as total revenue TR minus total cost TC TR TC Total revenue is equal to the product of price P and quantity Q TR P Q Total cost is given by the cost function CQ 400 05Q2 To find the profitmaximizing output we need to find the quantity at which marginal revenue MR equals marginal cost MC Marginal revenue is the derivative of total revenue with respect to quantity and marginal cost is the derivative of total cost with respect to quantity MR dTRdQ MC dTCdQ MR is equal to the price for a perfectly competitive firm so MR P Setting MR equal to MC we have P MC To find the quantity at which MR equals MC we differentiate the cost function CQ with respect to Q MC dCQdQ d400 05Q2dQ 0 1 05 2Q Q Setting P equal to MC we have P Q Since the price of similar products offered by Apple Samsung and other phones is 400 we set P 400 Q 400 Therefore the profitmaximizing output for RussCo Phone is Q 400 The price would also be 400 To calculate the profit ... View full answer

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