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# Cost function, average fixed cost, variable cost function

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2. You hire an intern from Southern University to help you analyze your production process, and she uses your historical cost records to estimate that your total cost function is C(Q) = 100 + 2Q + 3Q2. Using this equation, answer the following and show your logic and calculations.
a. How much is your firm's profit or loss at an output of zero? Explain.
b. With the above cost equation, average total costs (ATC), first decline as output increases, and then begin to rise. Assuming output occurs in whole units, i.e. 1, 2,3,... at what output does the low point of ATC occur and what is the ATC at that output? Show your calculations.
c. What is the variable cost of an output of 50?
d. What are Average Fixed Costs (AFC) at a production level of 10?

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#### Solution Preview

a) At zero output cost C(Q=0)=100+2*0+3*0^2=100
Revenue = Price*0 units = 0
Profits = Revenues - cost = 0-100= -100 (loss of 100)

b) ...

#### Solution Summary

Provides step-by-step solution to the production function and profitability concepts for easy understanding.

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## Managerial Economics: Cost Function

1. An economist estimated that the cost function of a single product is
C(Q)= 50 +25Q+30Q SQUARED+5Q CUBED
Based on this information determine:
a. The fixed cost of producing 10 units of output.
b. The variable cost of producing 10 units of output.
c. The total cost of producing 10 units of output.
d. The average fixed cost of producing 10 units of output.
e. The average variable cost of producing 10 units of output.
f. The average total cost of producing 10 units of output.
g. The marginal cost when Q = 10.

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