Verification of Profit-Maximization Tangency
A firm faces an inverse demand curve given by the equation P = 44 - 0.5Q and has a marginal cost function of MC = 2 + 0.4Q. The firm's profit-maximizing point has been identified as an output of Q = 30 and a price of P = 29.
For profit maximization, the slope of the firm's isoprofit curve must be equal to the slope of the demand curve at this optimal point. Using the provided information, calculate the slope of the isoprofit curve at the profit-maximizing point to verify that this condition is satisfied. Show your work.
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Verification of Profit-Maximization Tangency
A firm faces an inverse demand curve of P = 44 - 0.5Q and has a cost function of C(Q) = 320 + 2Q + 0.2Q². The firm's profit-maximizing output is Q=30, which corresponds to a price of P=29. At this specific point (Q=30, P=29), what is the relationship between the slope of the firm's isoprofit curve and the slope of the demand curve?
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