# Analyzing the given cost functions

Suppose that the manager of a firm operating in competitive market has estimated the firm's average variable cost function to be AVC=4000-5Q+0.002Q^2

Total fixed cost is $62500. The firm across the street is charging $1000 per unit that they sell.

a. What is the minimum value for AVC?

b. How much output should the firm produce in the short run?

c. How much profit will the firm earn?

Hint: if we face the following quadratic equation: ax^2+bx+c=0, then we can find x using this formula

x=(-b+-(b^2-4ac))/2a.

Use the largest number as your solution

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#### Solution Preview

a. What is the minimum value for AVC?

AVC=4000-5Q+0.002Q^2

d(AVC)/dQ=-5+0.004Q

For fining minimum value of AVC put d(AVC)/dQ=0

-5+0.004Q=0

Q=1250

Find second derivative of AVC

d^2(AVC)/dQ^2=0.004

It is a positive value, ...

#### Solution Summary

Solution describes the steps to calculate minimum value of AVC, optimal output and profit at optimal output level.