# What Is a Constant Elasticity of Substitution?

Ray Hawk

The constant elasticity of substitution (CES) is a method in econometrics for a family of price indicators based on a substitution of input values or products. It is a method of calculating output productivity by substituting inputs. Commonly, a scarce factor of production is substituted for an abundant one, with a prominent example in the constant elasticity of substitution being the trade-off between labor and capital. The constant elasticity of substitution (CES) is a method in econometrics for a family of price indicators based on a substitution of input values or products.

The mathematics and statistics of economics can be very complex. Formulas such as the constant elasticity of substitution are often made into a computer function that can then graph visual results, as parameters such as productivity factors and the elasticity of substitution are accounted for. The CES function in this regard is rivaled by the Cobb-Douglas specification. Cobb-Douglas is often seen as too restrictive when factoring in elements, such as taxes on labor and capital, however, and the less-restrictive nature of CES appears to produce more accurate results.

Production economics and business cycle analyses traditionally rely on substituting scarce factors with abundant ones to drive economic growth. These approaches are most often seen in national macroeconomic theory and policies rather than being applied by individual corporations. The level of constant elasticity of substitution directly affects economic growth, and this has been established in models since at least 1956. Cobb-Douglas calculations have long been used as a model for United States economic growth, but empirical evidence has questioned some of the validity of the results, and constant elasticity of substitution has been gaining favor over it with economists in recent years.

Consumer theory of economics cannot be broken down to mathematical functions such as CES or Cobb-Douglas without missing many of the unpredictable interactions that take place in a real economy. Despite this, the models are considered capable of drawing valuable inferences, even if the input parameters used are statistical artifacts. The constant elasticity of substitution accounts for some variables by using normalization and aggregation techniques not present in the original form of the theory. The estimates of these utility functions are meant, in fact, to take input values and project maximum potential output, not real-world actual output.

Projected maximum output calculated by the constant elasticity of substitution is known as a production possibility frontier (PPF). When PPFs for a majority of individual corporations are added together, an estimated PPF for an entire economy can be determined. A very strict definition of inputs such as those of aggregate capital must be used for meaningful PPF results. Problems do arise, however, when capital is defined in monetary units that rise and fall with interest rates.

Fluctuating capital values are one example of the marginal rate of technical substitution (MRTS) effect. Aggregation is only valid if the MRTS variability of the input has no effect on the calculation for maximum potential output. Aside from interest rates affecting the valuation of capital, another example of a factor that could invalidate results in the constant elasticity of substitution is technological change, which can augment labor and alter its production function.

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