Microsoft wants to estimate the average variable cost function of producing comp

Question

Microsoft wants to estimate the average variable cost function of producing computer diskettes. The firm believes that AVC varies with the level of output and wages. Alan Anderson, the economist in the research department of the firm, collects monthly data on output (the number of diskettes produced), average variable costs, and wage rates paid by the firm over the past two years. He deflates costs and wages by their respective price indexes in order to eliminate inflationary influences. He then regresses total variable costs (TVC) on output (Q) and wages (W) and obtains the following result (where the numbers in parentheses are t values) TVC = 0.14 + 0 80 Q + 0.036 W (2.8) (3.8) (3.3) R - 2 = 0.92 D - W = 1.9. (a). If W = $10, derive the AVC and MC functions of the firm. (b). What are the shapes of the AVC and MC curves of the firm? (c). Why did Anderson fit a linear rather than a quadratic or cubic TVC function? (d). Was this the right choice? Why?

Explanation / Answer

a) TVC is given by the equation in the example.

Now AVC = TVC / Q

AVC = (0.14+ 0.80Q + 0.036W * 2.8 * 3.8 * 3.3 *R - 2) /Q = ( 0.92D -W) /Q = 1.9 /Q

Now W is given as 10

0.92D - 10 = 1.9

D = 12.93

Marginal cost is the first derivative of the cost function

dTVC / dQ = MC

b) AVC and MC shows a U shaped curve as increasing output decreases AVC and MC. However, after a point it again starts to increase proving the law of diminishing return.

c) Anderson has considered that AVC and MC will change in proportion with output after deflating with relative indexes.

d) Assuming AVC and MC linear is wrong choice for the reason that they typically show U-shaped curve. As the output increases, AVC and MC decreases upto the the point where law of diminishing return gets activated.

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