Answer to Question #221179 in Microeconomics for Vickie

Question

The Cobb Douglas production function is given by f(X1,X2)=Ax1,X2b it turns out that's the type of returns to scale of the function will depend on the magnitude of (a + b) which values of (a + b) will be associated with the different kinds of returns to the scale to demonstrate his illustration
Listen aided example of Edgeworth box illustrate how to prove the Pareto efficiency general equilibrium is achieved

Answer 1

COBB homogenous equation is Q=AKβLα

Where,

Q is the output

A is the efficiency parameter

K, L is capital and labor

α is the elasticity of output relative to labor

β is the elasticity output relative to capital

features or properties

1.     The values of α+ β gives return scale types

                               i.           If α+ β=1 it is constant to return scale

                             ii.           If α+ β>1 it is rising returns to scale

                           iii.           If α+ β<1 it is decreasing returns to scale

2.     Factor intensity

Within the cobb-douglas function factor intensity is computed by the ratio α/ β, the higher the ratio, the more labor intensive the technique. The lower the ratio, the more capital intensive the technique.

3.     Slope of the cobb-douglas production equation

MRTS=MPL/MPK