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One and Only, Inc., is a monopolist. The demand function for its product is estimated to

Q = 60 - 0.4P + 6Y +2A

where Q = quantity of units sold
P = price per unit
Y = per capita disposable personal income (thousands of dollars)
A = hundreds of dollars of advertising expenditures

The firm's average variable cost function is

AVC = Q^2 - 10Q + 60

Y is equal to 3 (thousand) and A is equal to 3 (hundred) for the period being analyzed.

a. If fixed costs are equal to $1,000, derive the firm's total cost function and marginal cost function.
b. Derive a total revenue function and marginal revenue function for the firm.
c. Calculate the profit-maximizing level of price an output for One and Only.
d. What profit or loss will One and Only earn?
e. If fixed costs were $1,200, how would your answers change fro Parts (a) through (d)?

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Solution Summary

Total Cost (TC) is determined in this case.

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a. If fixed costs are equal to $1,000, derive the firm's total cost function and marginal cost function.
AVC = Q^2 - 10Q + 60

We know that TVC=AVC*Q=Q^3-10Q^2+60Q

Total Cost (TC)=Total fixed costs+ Total Variable Costs

TC=1000+Q^3-10Q^2+60Q
TC=1000+60Q-10Q^2+Q^3 -------(1)

Marginal Cost=MC=d(TC)/dQ=60-20Q+3Q^2

b. Derive a total revenue function and marginal revenue function for the firm.
Q = 60 ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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