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One of the most common is the Cobb-Douglas utility function, which has the form u(x, y) = x ^a y ^{1 - a}. Another common form for utility is the Constant Elasticity of Substitution (CES) utility function. ... The curve in the figure shows a many combinations of commodities X and Y that all result in the same utility.

The powers of labor and capital (that are β and α) in the C-D production function measure output elasticities of labor (L) and capital (K) respectively. The output elasticity of a factor shows the percentage change in output due to a given percentage change in the number of factor inputs.

From these figures you can also see that: (1) demands derived from a Cobb–Douglas utility function have no cross-price effects and (2) good 1 and good 2 are both normal goods for the consumer (and, because of this, both are also ordinary goods).

Since, the Cobb-Douglas (CD) function has been (and is still) abundantly used by economists because it has the advantage of algebraic tractability and of providing a fairly good approximation of the production process. Its main limitation is to impose an arbitrary level for substitution possibilities between inputs.Sep 29, 2014

If our f(x, y) = cxayb exhibits constant or decreasing return to scale (CRS or DRS), that is a + b ≤ 1, then clearly a ≤ 0, b ≤ 0, and we have thus the Cobb-Douglas function is concave if and M1 ≤ 0, M1 ≤ 0, M2 ≥ 0, thus f is concave.

The Cobb-Douglas production function is based on the empirical study of the American manufacturing industry made by Paul H. ... It is a linear homogeneous production function of degree one which takes into account two inputs, labour and capital, for the entire output of the . manufacturing industry.

Cobb-Douglas production function refers to the production function in which one input can be substituted by other but to a limited extent. For example, capital and labor can be used as a substitute of each other, but to a limited extent only. Cobb-Douglas production function can be expressed as follows: Q = AK^aL^b.

The Cobb-Douglas utility results in constant expenditure shares. When two goods are perfect complements, they are consumed proportionately. Perfect complements boil down to a single good problem. A bliss point, or satiation, is a point at which further increases in consumption reduce utility.

Constant Returns to Scale

For example, if twice the inputs are used in production, the output also doubles. ... A regular example of constant returns to scale is the commonly used Cobb-Douglas Production Function (CDPF).