Question

The cost function (monthly) for your company can be defined as; TC = cost per unit (AC) * quantity supplied (Q). If the cost per unit (average cost) for your firm is AC = (800/Q) – 10 +2Q:

a. What is the total cost function for your firm in terms of Q?

b. How would you interpret the intercept term in this function?

c. What is the marginal cost function for your firm?

d. At what level of output (Q) is AC minimized?

e. Is MC always less than AC?

f. Combine the total revenue function from problem 1 and total cost function from this problem and derive the profit-maximizing level of output and the price that would be charged.

g. Why is the output level at this point smaller than the output level that maximizes total revenue?

Answer 1

Answer

(a)

AC = (800/Q) – 10 +2Q

=> TC = AC*Q

=> TC = ((800/Q) – 10 +2Q)Q  

=> TC = 800 – 10Q +2Q² -----------------------Total Cost Function

(b)

We can see from the above function that intercept = 800 when Output = 0. Means Firm will have to incur 800 even if it is not producing anything or we can say that intercept = 800 is independent of output. This is what we called fixed cost. Hence intercept term represents Fixed Cost which is equal to 800.

(c)

MC = dTC/dQ = -10 + 4Q

=> MC = -10 + 4Q --------------Marginal Cost Function

(d)

Min: AC = (800/Q) – 10 +2Q

First order condition:

d(AC)/dQ = 0 => 800/(Q)² = 2 => Q = 20

Hence, AC is minimum when Q = 20

(e)

MC is less than AC when AC is falling and MC is greater than AC when AC is rising and MC = AC when AC is at its minimum.

Hence,MC is lesser than AC when Q < 20 , MC is greater than AC when Q > 20.

Hence, MC is not always lesser than AC