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SUPPOSE A FIRM’S TOTAL COST CURVE IS TC=150^2+8Q+135,WHAT IS THE OUTPUT LEVEL THAT MINIMIZES AVERAGE TOTAL COST

Answer:

Calculating Output Level to Minimize Average Total Cost

The output level that minimizes average total cost can be calculated by setting the average total cost (ATC) equal to zero and solving for the quantity of output (Q). The average total cost is calculated by dividing the total cost (TC) by the quantity of output (Q). In this example, the total cost is given by the expression TC=150²+8Q+135. To minimize the average total cost, set the expression for the average total cost equal to zero and solve for Q:

ATC = 0 = (150²+8Q+135)/Q

To solve for Q, multiply both sides of the equation by Q and simplify:

0 = 150²+8Q²+135Q

Since the left side of the equation is equal to zero, subtract both sides of the equation by 150²+135Q and simplify:

-150²-135Q = -8Q²

To solve for Q, divide both sides of the equation by -8 and simplify:

Q² + 16.875Q + 18.75 = 0

Using the quadratic formula, the solution for Q is:

Q = [-16.875 ± √(16.875²-4(1)(18.75))]/2(1)

The output level that minimizes average total cost is Q = 6.375.

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