Microeconomy Question

Question

Consider a production function of the form

f(x1,x2) = x₁^α + x₂^α

with 0 < α.

1.    For which values of α will this exhibit constant, increasing and decreasing Returns to Scale?

2.    What is the TRS (Technical Rate of Substitution)?

3.    What is the Elasticity of Substitution?

Now consider the CES (Constant Elasticity of Substitution) production function

g(x1,x2) = (x₁^α + x₂^α)^1/α

4.    What is the Return to Scale for the production function g?

5.    What is the TRS and the Elasticity of Substitution for the CES production?

Answer 1

Returns to scale are determined by analyzing the firm's LR production function.There is no direct correlation between increasing. decreasing and constant returns to scale and marginal product of input. A production function can have increasing returns even though MP of each input increases as more of the input is used.

Returns to scale exhibits a LR phenomenon, while MP describes a change in a single input( SR).

MRS measures the amount of K that can be saved by applying an extra unit of labor.

The input bundles in the equation f(x1,x2) = x₁^α + x₂^α

with 0 < α.

exhibits decreasing returns to scale, that means doubling input levels less than doubles output.

Elasticity of Substitution Elasticity of Substitution= % Change in K/L% Change in Slope of Isoquant