# Marginal and average cost functions

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.

https://brainmass.com/economics/pricing-output-decisions/marginal-average-cost-functions-400863

#### Solution Preview

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 Summary

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

$2.19