Question

1.     Suppose a firm sells good X in a perfectly competitive market its per unit price is 11 birr and the total cost of producing good X is given by TC = 1/3Q³ – 3Q² 20Q + 100, then answer the following questions.

a)     What is average variable cost when Q=5

b)     What is the total fixed cost when Q=0

c)     What is marginal cost when Q=6

Answer 1

Solution:

a.). Average variable cost when Q = 5:

AVC = $\frac{TVC}{Q}$

TVC = 1/3Q³ – 3Q² + 20Q

AVC = $\frac{\frac{1}{3}Q^{3} - 3Q^{2} + 20Q}{Q} = \frac{1}{3}Q^{2} - 3Q + 20$

When Q = 5:

$\frac{1}{3}(5)^{2} - 3(5) + 20 = 8.33 - 75 + 20 = (46.67)$

Average variable cost when Q = 5: = (46.67)

b.). What is the total fixed cost when Q=0:

The total fixed cost when Q = 0: = 100

 

c.). What is marginal cost when Q=6:

TC = 1/3Q³ – 3Q² + 20Q + 100

MC = $\frac{\partial TC}{\partial Q} =$ $Q^{2} - 6Q + 20$

When Q = 6:

= 6² – 6(6) + 20 = 36 – 36 + 20 = 20

The marginal cost when Q=6: = 20