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# Total cost function and the production line

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1. A company produces table and chairs with the following total cost function TC=10,000+10Q+0.1Q2 in which Q=quantity of chairs produced. If the company can sell as many chairs it wishes at the current market price of \$45, how many chairs should it produce to maximize its short-run profits?

2. A production with the form Q=150L.75 K.50 will have? In the long run? a. increasing returns to scale, b. decreasing returns to scale, c. constant returns to scale, d. diminishing returns to the variable input

#### Solution Preview

Question 1
Maximum short-run profits: Total revenues = Total costs
Total revenue = \$45Q
Total cost = 10,000 + 10Q + 0.1Q2
Maximum short-run profits: \$45Q - (10,000 + 10Q + 0.1Q2)
Maximum short-run profits: \$45Q - 10,000 - 10Q - 0.1Q2)
Maximum short-run profits: \$35Q - 10,000 - 0.1Q2
Derivative of Maximum short-run profits: \$35Q - 10,000 - 0.1Q2
Maximum short-run profits: 35 - 0 - ...

#### Solution Summary

Compute the output or quantity that maximizes short-run profits.
When is a production classified as increasing returns to scale, decreasing returns to scale, constant returns to scale or diminishing returns to the variable input?

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