Key Terms and Concepts

amount of another input to maintain a given level of output.If capital and labor are substitutable,the marginal rate of technical substitution is defined as the ratio of the marginal product of labor to the marginalproductof capital,that is, MPL/MPK.

Returnstoscale refers to the proportional increase in output given an equal proportional increase in all inputs.Since all inputs are variable, “returns to scale”is a long-run production phenomenon. Increasingreturns toscale (IRTS) occur when a proportional increase in all inputs results in a more than proportional increase in output. Constantreturnstoscale (CRTS) occur when a proportional increase in all inputs results in the same proportional increase in output. Decreasingreturnstoscale (DRTS) occur when a proportional increase in all inputs results in a less than proportional increase in output.

Another way to measure returns to scale is the coefficient of output elasticity (eQ),which is defined as the percentage increase (decrease) in output with respect to a percentage increase (decrease) in all inputs.The coefficient of output elasticity is equal to the sum of the output elasticity of labor (eL) and the output elasticity of capital (eK),that is, eQ =eL +eK. IRTS occurs when eQ > 1. CRTS occurs when eQ = 1. DRTS occurs when eQ < 1.

The Cobb–Douglasproductionfunction is the most popular specification in empirical research.Its appeal is largely the desirable mathematical properties it exhibits,including substitutability between and among inputs, conformity to the law of diminishing returns to a variable input,and returns to scale.The Cobb–Douglas production function has several shortcomings, however,including an inability to show marginal product in stages I and III.

Most empirical studies of cost functions use time series accounting data, which present a number of problems.Accounting data,for example,tend to ignore opportunity costs,the effects of changes in inflation,tax rates, social security contributions,labor insurance costs,accounting practices,and so on.There are also other problems associated with the use of accounting data including output heterogeneity and asynchronous timing of costs.

Economic theory suggests that short-run total cost as a function of output first increases at an increasing rate,then increases at a decreasing rate.Cubic cost functions exhibit this theoretical relationship,as well as the expected “U-shaped”average total,average variable,and marginal cost curves.

KEY TERMS AND CONCEPTS

Averageproductofcapital(APK) The total product per unit of capital usage.It is the total product of capital divided by the total amount of capital employed by the firm.

Averageproductoflabor(APL) The total product per unit of labor usage.

It is the total product of labor divided by the total amount of labor employed by the firm. Cobb–Douglasproductionfunction It may not in practice be possible precisely to define the mathematical relationship between the output of a good or service and a set of productive inputs employed by the firm to produce that good or service.In spite of this,because of certain desirable mathematical properties,perhaps the most widely used functional form to approximate the relationship between the production of a good or service and a set of productive inputs is the Cobb–Douglas production function.For the two-input case (capital and labor),the

Cobb–Douglas production function is given by the expression Q =

AKaLb . Coefficientofoutputelasticity The percentage change in the output of a good or service given a percentage change in all productive inputs.Since all inputs are variable,the coefficient of output elasticity is a long-run production concept. Constantreturnstoscale(CRTS) The case in which the output of a good or a service increases in the same proportion as the proportional increase in all factors of production.Since all inputs are variable, CRTS is a longrun production concept.In the case of CRTS the coefficient of output elasticity is equal to unity. Decreasingreturnstoscale(DRTS) The case in which the output of a good or a service increases less than proportionally to a proportional increase in all factors of production used to produce that good or service.Since all inputs are variable, DRTS is a long-run production concept.In the case of DRTS the coefficient of output elasticity is less than unity. Factorofproduction Inputs used in the production of a good or service.

Factors of production are typically classified as land,labor,capital,and entrepreneurial ability. Increasingreturnstoscale(IRTS) The case in which the output of a good or a service increases more than proportionally to a proportional increase in all factors of production used to produce that good or service.

Since all inputs are variable, IRTS is a long-run production concept.In the case of IRTS the coefficient of output elasticity is greater than unity. Isoquant A curve that defines the different combinations of capital and labor (or any other input combination in n-dimensional space) necessary to produce a given level of output. Lawofdiminishingmarginalproduct As increasing amounts of a variable input are combined with one or more fixed inputs,at some point the marginal product of the variable input will begin to decline.Because at least one factor of production is held fixed,the law of diminishing returns is a short-run concept.

Longruninproduction In the long run,all factors of production are variable. Marginalproductofcapital(MPk) The incremental change in output associated with an incremental change in the amount of capital usage.

If the production function is given as Q = f(K, L),then the marginal product of capital is the first partial derivative of the production function with respect to capital (∂Q/∂K),which is assumed to be positive. Marginalproductoflabor(MPL) The incremental change in output associated with an incremental change in the amount of labor usage.If the production function is given as Q = f(K, L),then the marginal product of labor is the first partial derivative of the production function with respect to labor (∂Q/∂L),which is assumed to be positive. Marginalrateoftechnicalsubstitution(MRTSKL) Suppose that output is a function of variable labor and capital input, Q = f(K, L).The marginal rate of technical substitution is the rate at which capital (labor) must be substituted for labor (capital) to maintain a given level of output.The marginal rate of technical substitution,which is the slope of the isoquant, is the ratio of the marginal product of labor to the marginal product of capital (MPL/MPK). Production function A mathematical expression that relates the maximum amount of a good or service that can be produced with a set of factors of production. Q = AKaLb The Cobb–Douglas production function,which asserts that the output of a good or a service as a multiplicative function of capital (K) and labor (L). Shortruninproduction That period of time during which at least one factor of production is constant. StageIofproduction Assuming that output is a function of variable labor and fixed capital,this is the range of labor usage in which the average product of labor is increasing.Over this range of output,the marginal product of labor 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).According to economic theory,production in the short run for a “rational”firm takes place in stage II of production. StageIIofproduction Assuming that output is a function of variable labor and fixed capital,this is the range of output in which the average product of labor is declining and the marginal product of labor is positive.Stage II of production begins where APL is maximized,and ends with MPL = 0. StageIIIofproduction Assuming that output is a function of variable labor and fixed capital,this is the range of production in which the marginal product of labor is negative.