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Marginal and average cost functions

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Given that the total cost function is:

TC = 100Q-Q^2+1/3 Q^3
where Q = rate of output and TC = total cost

a. Determine the marginal and average cost functions.
b. Calculate the output level that minimizes average cost.
c. Calculate the output level that minimizes marginal cost.

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Solution Summary

Solution determines the marginal and average cost functions. It also determines the output levels which minimize average and marginal costs.

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a. Determine the marginal and average cost functions. SHOW WORK

TC = 100Q-Q^2 + 1/3 Q^3

ATC=TC/Q=(100Q-Q^2+1/3Q^3)/Q=100-Q+1/3 Q^2

MC=d(TC)/dQ= d(100Q-Q2 + 1/3 Q3)/dQ=100-2Q+Q^2 ...

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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