Evaluating a Production Decision
A manager at a firm with the inverse demand curve P = 44 - 0.5Q and cost function C(Q) = 320 + 2Q + 0.2Q² is currently producing a quantity of Q=20, which results in a price of P=34. The manager claims this is the profit-maximizing output. Using the principle that profit is maximized where the slope of the isoprofit curve is tangent to the slope of the demand curve, evaluate the manager's claim. Is the firm maximizing its profit at Q=20? Justify your answer by calculating and comparing the relevant slopes at this point.
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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?
Evaluating a Production Decision
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Consider a firm facing an inverse demand curve represented by the equation P = 44 - 0.5Q. True or False: The slope of any of the firm's isoprofit curves will be equal to -0.5 at every point where the isoprofit curve intersects the demand curve.
A profit-maximizing firm operates with an inverse demand function of P = 44 - 0.5Q. At the point of optimal output and price, the slope of the firm's isoprofit curve must be tangent to the demand curve. Therefore, the value of the isoprofit curve's slope at this specific point must be ____.
A firm's production is described by the inverse demand function P = 44 - 0.5Q. Match each economic concept related to this firm's profit maximization with its correct description or value.
A firm faces an inverse demand curve given by P = 44 - 0.5Q. The slope of this demand curve is a constant -0.5. The firm is currently producing at a point where its quantity is 20 and the corresponding price is 34. At this specific point (Q=20, P=34), the slope of the firm's isoprofit curve is -1.2. Based on a comparison of these slopes, what action should the firm take to increase its profit?
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Analysis of a Firm's Production Point