Question

The Cobb- Douglas production function is given by the form Y = ALαKβ

Where, Y = Output (mt/day), L = Labour (hours/mt) K = Capita (Rs/mt). By taking the natural logarithm of each term in the function, that is LnY = LnA+αLnL+βLnK. Using a standard multiple linear regression model the parameters of the function were obtained as follows;

Ln Y = 1.389 +0.8LnL + 0.6LnK

            (0.53)    (0.02)      (0.04)

Answer 1

Elasticity of labour $=$ $\frac{dY}{DL}$ $\times$ $\frac{L}{Y}$

Now;

In Y $=$ 1.388+0.8lnL + 0.6ln K

Differentiating both sides w.r.t. labour we get:

$\frac{1}{Y}$ $\times$ $\frac{dY}{DL}=$ $\frac{0.8}{L}$

$\frac{dY}{dL}=$ $\frac{0.8Y}{L}$

Putting this value in elasticity equation:

E(L)=$\frac{0.8Y}{L}$ $\times$ $\frac{L}{Y}$

E(L)=0.8

Hence the change in the rate of labor leads to 0.8 change in the level of output

Similarly,

Elasticity of labor =$\frac{dY}{dK}\times\frac{K}{Y}$

Differentiating output equation w.r.t to capital we get

$\frac{1}{Y}\times\frac{dY}{dK}=\frac{0.6}{K}$

Putting in elasticity equation we get;

E(K)=$\frac{0.6Y}{K}\times\frac{K}{Y}$

E(K)=0.6

Hence the change in the rate of capital leads to 0.6 change in the level of output.