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Deriving Marginal cost and revenue functions

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The Madison Corporation, a monopolist, receives a report from a consulting firm concluding that the demand function for its product is
Q=78 - 1.1P + 2.3Y +0.9A
Where Q is the number of units sold, P is the price of its product (in dollars); Y is the per capita income (in thousands of dollars), and A is the firm's advertising expenditure (in the thousands). The firm's average variable cost function is

AVC=42 - 8Q + 1.5 Q2

Where AVC is average variable cost (in dollars)

a. Can one determine the firm's marginal cost curve?
b. Can one determine the firm's marginal revenue curve?
c. If per capita income is $4,000 and advertising expenditure is $200,000, can one determine the price and output where marginal revenue equals marginal cost? If so, what are they?

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Solution Summary

Solution describes the methodology for deriving firm's marginal and marginal revenue curves.

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Solution:

a. Can one determine the firm's marginal cost curve?

AVC = 42-8Q+1.5Q^2
Total variable cost = AVC*Q
= (42-8Q+1.5Q^2)*Q
=42Q-8Q^2+1.5Q^3
Marginal cost = d(Total Cost)/dQ
= d(TVC)/dQ
= 42-16Q+4.5Q^2 ...

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  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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