The total fixed cost (TFC) and total cost (TC) functions of a hypothetical firm are shown in the graph below. Study it and answer the questions that follow:
(a) Determine the firm’s
(i) variable cost at output levels 2, 4 and 6
(ii) average total cost at output levels 2 and 3
(iii) marginal cost at output levels 4 and 6
(b) If the price of the firm’s product is $40, calculate the firm’s profit or loss when the following units are sold:
(i) 2 units; (ii) 4 units
Explanation
(a) (i) VC = TC - TFC, TFC = $40
VC\(_2\) = 100-40 = $60
VC\(^4\) = 140-40 = $100
VC\(_6\) = 180-40 = $140
(ii) ATC\(_2\) = \(\frac{TC}{Q}\)
ATC\(_2\) = \(\frac{100}{2}\) = $50
ATC\(_3\) = \(\frac{120}{3}\) = $40
(iii) MC = \(\frac{\DeltaTC}{\Delta Q}\)
MC\(_4\) = \(\frac{TC_4 - TC_3}{Q_4 - Q_3}\) = \(\frac{140- 120}{1}\) = $20
MC\(^6\) = \(\frac{TC_6 - TC_5}{Q_6 - Q_5}\) = \(\frac{180- 160}{6-5}\) = $20
(b) (i) Profit = Total Revenue - Total Cost
=TR-TC
TR = Price x Quantity
= P x Q
When 2 units are sold,
Profit = ($40 x 2) - $100
= $80 - $100
= -$20 (Loss)
(ii) When 4 units are sold,
Profit = ($40 x 4) - $140
= $160 - $140
= $20