Cost Curve - Short-run Average Total Cost Curve (SRATC or SRAC)

Short-run Average Total Cost Curve (SRATC or SRAC)

The average total cost curve is constructed to capture the relation between cost per unit of output and the level of output, ceteris paribus. A perfectly competitive and productively efficient firm organizes its factors of production in such a way that the average cost of production is at the lowest point. In the short run, when at least one factor of production is fixed, this occurs at the output level where it has enjoyed all possible average cost gains from increasing production. This is at the minimum point in the diagram on the right.

Short-run total cost is given by

STC = P_KK+P_LL,

where P_K is the unit price of using physical capital per unit time, P_L is the unit price of labor per unit time (the wage rate), K is the quantity of physical capital used, and L is the quantity of labor used. From this we obtain short-run average cost, denoted either SATC or SAC, as STC / Q:

SRATC or SRAC = P_KK/Q + P_LL/Q = P_K / AP_K + P_L / AP_L,

where AP_K = Q/K is the average product of capital and AP_L = Q/L is the average product of labor.

Short run average cost equals average fixed costs plus average variable costs. Average fixed cost continuously falls as production increases in the short run, because K is fixed in the short run. The shape of the average variable cost curve is directly determined by increasing and then diminishing marginal returns to the variable input (conventionally labor).