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Suppose that a monopolist's inverse demand curve can be expressed as:
P = 10,000 + 100Q - 10Q2.
The monopolist's total cost curve is:
TC = 5,000Q.
a. Use calculus to determine the monopolist's marginal revenue curve.
b. Use calculus to determine the monopolist's marginal cost curve.
c. What is the monopolist's profit-maximizing level of output?
d. What price should the monopolist charge to maximize its profit?
Total Revenue
The total income generated by a firm from selling its goods or services before any costs or expenses are deducted.
Output
The total amount of goods or services produced by a firm, industry, or economy over a specific period.
Average Total Cost
The total cost of production divided by the quantity of output, representing the per-unit cost of production.
Short Run
The short run in economics refers to a period during which at least one input, such as plant size, is fixed and cannot be changed by the firm.
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