Which of the following is true?
A) The Cobb-Douglas production function is given by the general formula $\mathrm { Q } = \mathrm { AL } \mathrm { K } ^ { \beta }$ and the constant elasticity of substitution is equal to 0 .
B) The Cobb-Douglas production function is given by the general formula $\mathrm { Q } = \mathrm { AL } \mathrm { K } ^ { \beta }$ and the constant elasticity of substitution is equal to 1 .
C) The Cobb-Douglas production function does not exhibit a constant elasticity of substitution.
D) The Cobb-Douglas production function always takes the form $Q = K ^ { 2 } L ^ { 2 }$.

Question

Which of the following is true? 
A) The Cobb-Douglas production function is given by the general formula $\mathrm { Q } = \mathrm { AL } \mathrm { K } ^ { \beta }$ and the constant elasticity of substitution is equal to 0 .
B) The Cobb-Douglas production function is given by the general formula $\mathrm { Q } = \mathrm { AL } \mathrm { K } ^ { \beta }$ and the constant elasticity of substitution is equal to 1 .
C) The Cobb-Douglas production function does not exhibit a constant elasticity of substitution.
D) The Cobb-Douglas production function always takes the form $Q = K ^ { 2 } L ^ { 2 }$.

Quizplus · Accepted Answer

The Cobb-Douglas production function is given by the general formula Q=AL^K^beta, where L and K represent labor and capital, respectively. The constant elasticity of substitution (CES) measures the responsiveness of the firm's input substitution to changes in input prices. The Cobb-Douglas production function exhibits a constant elasticity of substitution, which is equal to 1. Therefore, choice B is the correct answer. The Cobb-Douglas production function is given by the general formula $\mathrm { Q } = \mathrm { AL } \mathrm { K } ^ { \beta }$ and the constant elasticity of substitution (CES) is equal to 1. This means that the relative substitution between capital and labor is constant along any isoquant. The CES can also be expressed as the slope of the isoquant, which shows the marginal rate of technical substitution between capital and labor. In the case of the Cobb-Douglas function, the marginal rate of technical substitution is proportional to the ratio of capital and labor, raised to the power of the elasticity of substitution (in this case, equal to 1). Therefore, the Cobb-Douglas function does exhibit a constant elasticity of substitution. Choices A, C, and D are all incorrect because they do not accurately describe the properties of the Cobb-Douglas production function.

Which of the Following Is True? A) the Cobb-Douglas Q=ALKβ\mathrm { Q } = \mathrm { AL } \mathrm { K } ^ { \beta }Q=ALKβ

Which of the Following Is True?
A) the Cobb-Douglas $\mathrm { Q } = \mathrm { AL } \mathrm { K } ^ { \beta }$