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:...

The graph gives a flat total fixed cost line at \(TFC = \$40\) and a total cost curve TC whose plotted points can be read off as follows:

Output (units)	0	1	2	3	4	5	6	7
TC (\$)	40	80	100	120	140	160	180	200
TFC (\$)	40	40	40	40	40	40	40	40

(a)(i) Variable cost at outputs 2, 4 and 6

Variable cost is what is left of total cost after the fixed cost is removed, \(TVC = TC - TFC\):

\[TVC_2 = 100 - 40 = \$60\]\[TVC_4 = 140 - 40 = \$100\]\[TVC_6 = 180 - 40 = \$140\]

(a)(ii) Average total cost at outputs 2 and 3

Average total cost spreads total cost over the units produced, \(ATC = \dfrac{TC}{Q}\):

\[ATC_2 = \frac{100}{2} = \$50\]\[ATC_3 = \frac{120}{3} = \$40\]

(a)(iii) Marginal cost at outputs 4 and 6

Marginal cost is the extra cost of producing one more unit, \(MC = \dfrac{\Delta TC}{\Delta Q}\). Here each step is one unit, so it is the rise in TC from the previous output:

\[MC_4 = TC_4 - TC_3 = 140 - 120 = \$20\]\[MC_6 = TC_6 - TC_5 = 180 - 160 = \$20\]

(b) Profit or loss when the product sells at \(\$40\) per unit

Profit is total revenue minus total cost, where \(TR = P \times Q\) and \(P = \$40\).

(i) 2 units

\[TR = 40 \times 2 = \$80, \qquad TC = \$100\]\[\text{Profit} = 80 - 100 = -\$20\]

The firm makes a loss of \(\$20\), because at such a low output the \(\$40\) fixed cost is spread over too few units.

(ii) 4 units

\[TR = 40 \times 4 = \$160, \qquad TC = \$140\]\[\text{Profit} = 160 - 140 = \$20\]

The firm now makes a profit of \(\$20\). Raising output has turned the loss into a profit because total revenue rises faster than total cost once the fixed cost is shared over more units.