Question

Suppose that the short-run cost function for Jim and Hack’s Raft Company is

C

=

60

+

30

q

+

5

q

2

with marginal cost given by

MC

=

30

+

10

q

.

(a) Obtain equations for

AFC

,

AVC

and

AC

curves.

(b) Draw

AFC

,

AVC

,

MC

and

AC

curves based on their equations.

(c) Which of the above curves will shift if the government decided to impose a flat licensing

fee of $200 on the company? Briefly explain your answer.

Answer 1

(a)

Total cost C = 60 + 30q + 5q² ---------- ( 1 )

MC = 30 + 10q

Fixed cost is the cost involved in creating the product which is not dependent on the quantity of the output being produced.

Therefore, from the total cost equation from ( 1 ), we can derive that the total fixed cost function for Jim and Hack’s Raft Company is 60 ( since the other components of the cost function that are dependent of q )

Total FC = 60

Average fixed cost = Total Fixed cost / ouput produced

Average fixed cost (AFC)= 60 / q

Variable cost is the cost involved in creating the product which is dependent on the quantity of the output being produced.

Therefore, from the total cost equation from ( 1 ), we can derive that the total variable cost function for Jim and Hack’s Raft Company is 30q + 5q²( since these are the components of the cost function that are dependent of q )

Total variable cost = 30q + 5q²

Average variable cost = Total variable cost / ouput produced

Average variable cost = ( 30q + 5q² ) / q

Average variable cost (AVC) = 30 + 5q

Average cost = average fixed cost + average variable cost

Average cost = ( 60 / q ) + 30 + 5q

(b)

(c)

If government decides to impose a flat licensing fees of $200 on the company, the new total cost function becomes

C = 200 + 60 + 30q + 5q²

C = 260 + 30q + 5q²

MC = d(C) / dq

MC = 30 + 10q

AFC = 260 / q

AVC = 30 + 5q

AC = ( 260/q ) + 30 + 5q

We can see from the above cost functions that the only functions that change are the average fixed cost (AFC) and the average cost (AC) functions. This is because by levying a $200 licensing fees on the company, the govenrment has increased the fixed charge for the company. It is because of this increase in fixed cost that the average fixed cost and the average cost changes.