Question

Assume a firm's cost function is given by the following equation; TC = 100q + 100q^2.

a. Calculate the firms's MC function.

b. What is the firm's AC function?

Some cost structures allow for decreasing average costs as the level of production increases for the firm. For example, a firm that purchases a $10,000 machine will calculate an average cost of $10,000 if it only produces one unit of its product ($10,000/1 = $10,000). However if the firm produces 100 units then the average cost per unit will be $10,000/100 = $100. This behavior is called economies of scale as it refers to the cost efficiency of increasing the scale of production.

c. For the current problem, calculate average cost for q=10, q=100, and q=1000. Does this firm's cost structure exhibit economies of scale? Are the returns to scale increasing, decreasing, or constant?

Answer 1

A. Differentiating TC wrt Q we get

B. Average total cost is determined by dividing the TC by Q

Dividing TC by Q we get

C. When Q = 10,

ATC = 100 + 100*10 = 100 + 1000 = $ 1100

When, q = 100,

ATC = 100 + 100*100 = 100 + 10,000 = $ 10,100

When, Q = 1000

ATC = 100 + 100*1000 = 100 + 100,000 = $ 100,100

As we can see the ATC is increasing as quantity is increased thus, the cost structure doesn't exhibits economies of scale.

The returns to scale is decreasing returns to scale.

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