Production and Cost in the Short Run
Production and Cost in the Short Run

The production function gives the maximum amount of output that can be produced from any given combination of inputs, given the state of technology. The production function assumes technological efficiency in production, because technological efficiency occurs when the firm is producing the maximum possible output with a given combination of inputs. Economic efficiency occurs when a given output is being produced at the lowest possible total cost.

In the short run, at least one input is fixed. In the long run, all inputs are variable. This chapter examines the short-run situation when only one input is variable, labor (L), and one fixed, capital (K). In the short run, the total product curve, which is a graph of the short-run production relation <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073402818/459495/K_bar.jpg','popWin', 'width=145,height=97,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a> with Q on the vertical axis and L on the horizontal axis, gives the economically efficient amount of labor for any output level when capital is fixed at units. The average product of labor is the total product divided by the number of workers: AP = Q/L. The marginal product of labor is the additional output attributable to using one additional worker with the use of capital fixed: MP = ΔQ / ΔL. The law of diminishing marginal product states that as the number of units of the variable input increases, other inputs held constant, there exists a point beyond which the marginal product of the variable input declines. When marginal product is greater (less) than average product, average product is increasing (decreasing). When average product is at its maximum—that is, neither rising nor falling—marginal product equals average product.

In the short run when some inputs are fixed, short-run total cost (TC) is the sum of total variable cost (TVC) and total fixed cost (TFC):

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Average fixed cost is total fixed cost divided by output:

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Average variable cost is total variable cost divided by output:

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Average total cost is total cost divided by output:

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Short-run marginal cost (SMC) is the change in either total variable cost or total cost per unit change in output:

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A typical set of short-run cost curves is characterized by the following features: (1) AFC decreases continuously as output increases, (2) AVC is <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073402818/459485/union.jpg','popWin', 'width=59,height=79,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>-shaped,(3) ATC is <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073402818/459485/union.jpg','popWin', 'width=59,height=79,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a>-shaped and crosses both AVC and ATC at their minimum points, and (5) SMC lies below (above) both AVC and ATC over the output range for which these curves fall (rise).

The link between product curves and cost curves in the short run when one input is variable is reflected in the following relations:

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When MP (AP) is increasing, SMC (AVC) is decreasing. When MP (AP) is decreasing, SMC (AVC) is increasing. When MP equals AP at AP 's maximum value, SMC equals AVC at AVC's minimum value. Similar but not identical relations hold when more than one input is variable.