Which of the following statements are true regarding Cobb-Douglas production function?
(a) It is long period production function
(b) It is short period production function Output elasticities with respect to factors are constant
(c) It is based on increasing returns to scale
(d) Output elasticities with respect to factors are constant
Select the correct option:
- AOption (a)
(a) and (c)
- BOption (b)
(a) and (d)
- COption (c)
(b) and (c)
- DOption (d)
(c) and (d)
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Correct answer
(a) and (d)
Why this answer is correct
- The correct answer is (a) and (d).
Key Points
- Cobb - Douglas Production Function:
- Cobb - Douglas production function is named after Paul H. Douglas and C. W. Cobb.
- Q = ALα Cβ, where Q is output; L and С are inputs of labour and capital respectively. A, a and β are positive parameters where = α > 0, β > 0. A = total factor productivity.
- Q depends directly depends upon L and C. A is the residual known as 'technical change'.
- This is a long run production function.
- Cobb-Douglas production function exhibits three types of returns to scale:
- If a+b>1, there are increasing returns to scale.
- If a+b=1, there are constant returns to scale.
- If a+b<1, there are decreasing returns to scale.
- Elasticity of an output:
- Output elasticity is the percentual change in output in respond to a change in levels of either labor or capital.
- Output elasticity with respect to labor is constant and equal to β.
- If β is 0.4 and labor increases in 20%, output will increase 8%.
- α and β are output elasticities of capital and labor, and are constant.
Hence, among the given alternatives, only (a) and (d) are correct.