Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

152 COSTS OF PRODUCTION [CHAP. 7
7.7 THE LONG-RUN TOTAL COST CURVE
In Section 7.6 and Example 5 we saw that the LTC for any level of output can be obtained by multiplying
output by the LAC for that level of output. By plotting the LTC values for various levels of output and joining
these points, we get the LTC curve. The LTC curve shows the minimum total costs of producing each level of
output when any desired scale of plant can be built. The LTC curve is also given by a curve tangent to all the
short-run total cost (STC) curves representing all the alternative plant sizes that the firm could build in the long
run. Mathematically, the LTC curve is the envelope to the STC curves (see Problem 7.17).
The LAC and the LMC curves and the relationship between them could also be derived from the LTC
curve—just as the SAC and the SMC curves and the relationship between them were derived from the STC
curve in Example 3 (see Problem 7.18). In addition, from the relationship between the STC curves and the
LTC curve derived from them, we can explain the relationship between the SAC curves and the corresponding
LAC curve, and between the SMC curves and the corresponding LMC curve (see Problem 7.19).
Finally, Problems 7.20 to 7.24 show the relationship between production functions and cost curves.
7.8 THE COBB-DOUGLAS PRODUCTION FUNCTION
The Cobb-Douglas is the most widely used production function in empirical work. The function is
expressed by
Q ¼ AL a K b
where Q is output and L and K are inputs of labor and capital, respectively. A, a (alpha) and b (beta) are positive
parameters determined in each case by the data. The greater the value of A, the more advanced is the technology.
The parameter a measures the percentage increase in Q resulting from a 1% increase in L while holding K
constant. Similarly, b measures the percentage increase in Q resulting from a one-percent increase in K while
holding L constant. Thus, a and b are the output elasticity of L and K, respectively. If a þ b ¼ 1, there are
constant returns to scale; if a þ b . 1, there are increasing returns to scale; and if a þ b , 1, there are decreasing
returns to scale. For the Cobb-Douglas function, e LK ¼ 1.
EXAMPLE 6.
If A ¼ 10 and a ¼ b ¼ 1/2, we have
Q ¼ 10L 1=2 K 1=2
Since a þ b ¼ 1, this Cobb-Douglas exhibits constant returns to scale, so that its isoquants are equally spaced and parallel
along an expansion path that is a straight line from the origin. By holding K constant and by varying L, we generate the total
product of labor (TP L ) and, from it, the AP L and MP L . These curves exhibit only stage II of production (as in Fig. 6-14).
Furthermore, the AP L and MP L are functions of or depend only on K/L. (See Problems 7.25 to 7.28.) The same is true for K.
7.9 X-INEFFICIENCY
In Section 6.1, we defined production function as the technological relationship that shows the maximum
quantity of a commodity that can be produced per unit of time for each input combination. However, in many
real-world situations, neither labor nor management work as hard or as efficiently as they could, so that output is
not maximum. This was called X-inefficiency by Leibenstein, who first introduced the concept.
X-inefficiency often occurs because of lack of motivation due to the absence of incentives or competitive
pressures. For example, labor contracts often do not specify a job completely, leaving the amount and quality of
effort required open to interpretation. In such cases, labor and management often choose not to exert themselves
as much as they could, leading to X-inefficiency.
EXAMPLE 7. Considerable empirical evidence has been found to support the existence of X-inefficiency. For example,
Leibenstein pointed out the case of an Egyptian petroleum refinery that had half the productivity of another similar installation.
When new management was brought in, the productivity gap was quickly closed with the same labor force. For many
years business has known that productivity can be increased by providing employees with a sense of belonging and accomplishment,
but only recently has business come to fully appreciate the large potential gain possible by reducing
X-inefficiency (i.e., increasing X-efficiency).