# Cost Function: AVC, AFC, ATC & MC

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An accountant for a car rental company was recently asked to report the firm's cost of producing various levels of output. The accountant knows that the most recent estimate available of the firm's cost function is C(Q)=100+10Q+Q(squared)

Costs are measured in 1,000's of dollars & output is measured in 1,000's of hours rented.

1. What is the average fixed cost of producing 2 units of output?

2. What is the average variable cost of producing 2 units of output?

3. What is the average total cost of producing 2 units of output?

4. What is the marginal cost of producing 2 units of output?

5. What is the relation between the answers to a,b,& c? Is this a general property of average cost curves?

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#### Solution Preview

Hello Student,

Before answering this question you may want to remind yourself of what are the components of the cost function. You also may want to look at how Average Fixed Cost (AFC), Average Variable Cost (AVC), Average Total Cost (ATC) and Marginal Costs are calculated.

The cost function given in the question is C (Q) = 100 + 10Q + Q(squared) which is derived from the general cost function y = c + mx, where c is given as total fixed costs and mx is given as the variable costs; or as in the given function, the fixed cost component is equivalent to $100,000 and the variable cost component is equivalent to 10Q + Q squared.

In order to calculate average fixed costs, you normally divide total fixed costs by the number of output produced. This may be given as:

AFC = TFC / Q or as in the ...

#### Solution Summary

This solution provides you with step by step calculation for how to find the average fixed cost, average variable cost, average total cost & marginal cost given the cost function C(Q)=100+10Q+Q(squared). It also provides you with reference to a link that can help to answer the last question.

Production and Cost Analysis

Please see the attached document of an example

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