The total cost of a firm can be written as TC=3a+bQ+cQ2TC=3a+bQ+cQ2 with a,ba,b and cc being non-zero

Accounting Dec 08, 2020

The total cost of a firm can be written as TC=3a+bQ+cQ2TC=3a+bQ+cQ2 with a,ba,b and cc being non-zero. Where is the minimum efficient scale for this firm?

a. Q=0Q=0

b. Q=(b2c)Q=(b2c)

c. Q=(3ac)Q=(3ac)

d. Q=(3ac)12

Expert Solution

The correct answer is: d. Q=(3ac)12Q=(3ac)12

We have the total cost function as:

TC=3a+2Q+cQ2TC=3a+2Q+cQ2

We know that at the minimum of the average total cost curve, the marginal cost is equal to the average total cost.

The marginal cost is equal to:

MC=ΔTCΔQ=Q+2cQMC=ΔTCΔQ=Q+2cQ

The average total cost is:

ATC=TCQ=3aQ+b+cQATC=TCQ=3aQ+b+cQ

Equating the average total cost to the marginal cost:

3aQ+b+cQ=b+2cQ3aQ=cQcQ2=3aQ2=3acQ=(3ac)12

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