225
Chapter Review
TABLE 5.3
Cobb-Douglas production function and
returns to scale. a+b
Returns to scale
<1 =1 >1
Decreasing Constant Increasing
Q = AK a Lb we can derive Table 5.3
CHAPTER REVIEW A production function is the technological relationship between the maximum amount of output a firm can produce with a given combination of inputs (factors of production). The short run in production is defined as that period of time during which at least one factor of production is held fixed. The long run in production is defined as that period of time during which all factors of production are variable. In the short run, the firm is subject to the law of diminishing returns (sometimes referred to as the law of diminishing marginal product), which states that as additional units of a variable input are combined with one or more fixed inputs, at some point the additional output (marginal product) will start to diminish. The short-run production function is characterized by three stages of production. Assuming that output is a function of labor and a fixed amount of capital, stage I of production is the range of labor usage in which the average product of labor (APL) is increasing. Over this range of output, the marginal product of labor (MPL) is greater than the average product of labor. Stage I ends and stage II begins where the average product of labor is maximized (i.e., APL = MPL). Stage II of production is the range of output in which the average product of labor is declining and the marginal product of labor is positive. In other words, stage II of production begins where APL is maximized and ends with MPL = 0. Stage III of production is the range of product in which the marginal product of labor is negative. In stage II and stage III of production, APL > MPL. According to economic theory, production in the short run for a “rational” firm takes place in stage II. If we assume two factors of production, the marginal rate of technical substitution (MRTSKL) is the amount of a factor of production that must be added (subtracted) to compensate for a reduction (increase) in the
