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Finding costs and maximizing profits for a monopoly

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A monopolist has demand and cost curves given by:
Q = 1000 - 2P
TC = 5,000 + 10Q

Find average cost (AC), average variable cost (AVC), marginal cost (MC), marginal revenue (MR).

a. What is the quantity that maximizes profit? What is the revenue and profit at that point?
b. What is the quantity that maximizes revenue? What is the revenue and profit at that point?

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Solution Summary

Given only a monopolist's demand and total cost functions, this solution shows how to calculate average cost (AC), average variable cost (AVC), marginal cost (MC), marginal revenue (MR), profit-maximizing quantity and revenue-maximizing quantity. All calculations are shown in detail.

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TC = 5000 + 10Q
AC = TC/Q
AC = (5000 + 10Q)/Q
AC = 5000/Q + 10

TC = Fixed Cost (FC) + Total Variable Cost (TVC)
FC = 5000
TVC = 10Q
AVC = TVC/Q
AVC = 10Q/Q
AVC = 10

MC is the derivative of TC.
TC = 5000 + 10Q
MC = 10

Q = 1000 - ...

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