Dr. Gary Stone, Winthrop University
Derivation of a Firm’s 7 Short-Run Cost Curves
A firm has seven measures of its short-run costs. (The short-run is a period of time in which a
key factor of production, usually capital, is fixed for the firm.) This worksheet shows how to
derive these cost curves graphically. Assume the firm operates with a given stock of capital
and can vary the amount of labor it employs.
1. Total Fixed Cost (TFC). This shows the firm’s total expenditure on its fixed factors of
production. It does not change when the level of output (Q) changes. Thus, TFC is drawn
as a horizontal line at the level of TFC. Assume TFC = $1,000 per week.
2. Average Fixed Cost (AFC). AFC is the per unit expenditure of the firm on its fixed
factors of production. AFC = TFC/Q. Since TFC is constant, AFC always decreases as Q
increases. For Q = 100, AFC = $1,000/100 = $10. For Q = 200, AFC = $1,000/200 = $5.
3. Average Variable Cost (AVC). AVC is the labor cost per unit of output. There are two
ways to find the value of AVC. AVC = TVC/Q and AVC = wage/APP. Since the wage
paid to labor is assumed to be constant, the AVC curve can be derived from the APP
curve: if APP rises, AVC falls; if APP falls, AVC rises; if APP is maximized, AVC is
minimized. Assume the wage paid a unit of labor is $500 per week and that APP has a
maximum value of 20 units of output when the firm uses 10 units of labor.
AVC = $500/20 = $25 per unit of output. Thus, when the firm produces 200 units of
output (Q = labor x APP = 10 x 20 = 200), its AVC is minimized with a value of $25.
When Q = 200, TVC = Q x AVC = 200 x $25 = $5,000.
4. Average Total Cost (ATC). ATC is the cost per-unit of output. There are two ways of
finding the value of ATC. ATC = TC/Q and ATC = AVC + AFC. Since we already have
the shapes of the AVC and AFC curves, let’s just add the value of AVC to the value of
AFC at each Q-level to get the value of ATC at that Q-level. For example, when Q = 200
we know AFC = $5 and AVC = $25 so ATC = $30. The vertical gap between the ATC
and AVC curves is AFC which falls as Q increases.
5. Marginal Cost (MC). MC is the change in the firm’s TC resulting from a one-unit increase
in output. Since TFC does not change when the firm increases output, MC also is the
change in the firm’s TVC when an extra output unit is produced. Thus, MC = TC/Q =
TVC/Q. (MC is the slope of both the TC and the TVC curves.) There is another way of
finding MC: MC = wage/MPP. This last view allows us to quickly draw the MC curve: if
MPP is increasing, MC is decreasing; if MPP is decreasing, MC is increasing; if MPP
is maximized, MC is minimized.
6. Total Variable Cost (TVC). TVC shows the firm’s total expenditure on labor (its variable
input) at different Q-levels. There are two ways of finding the value of TVC.
TVC = labor x wage and TVC = Q x AVC. Because the firm must use more labor to
increase its output, TVC will increase as Q increases – the TVC curve always has a
positive slope. MC represents the slope of the TVC (MC = TVC/Q) so the Q-level
level where MC is minimized is where the slope of the TVC curve is minimized.
7. Total Cost (TC). The TC curve shows the total expense to the firm when it produces
different levels of output. Since TC = TFC + TVC, we simply add the values of TFC and
TVC at each output level to get the value of TC. Because TFC is a constant value the TC
and TVC curves are parallel vertically at all output levels. The constant vertical gap
between the TVC and TC curves represents TFC.
8. The “marginal-average” cost graph of a firm can be used to show all seven measures of
short-run cost for a firm at any given Q-level. At Q = 400:
(1) AVC is the vertical distance (ab) from the Q-axis to the AVC curve = $42.50.
(2) ATC is the vertical distance (ac) from the Q-axis to the ATC curve = $45.00.
(3) AFC is the vertical distance (bc) from the AVC curve to the ATC curve = $2.50.
(4) MC is the vertical distance (ad) from the Q-axis to the MC curve = $50.00.
(5) TVC is the rectangle (0abg) under the AVC curve = (400)($42.50) = $17,000.
(6) TC is the rectangle (0acf) under the ATC curve = (400)($45.00) = $18,000.
(7) TFC is the rectangle (gbcf) between the TVC rectangle and the TC rectangle =
(400)($2.50) = $1,000.