Question

If a CobbDouglas production function has alpha​ = 0.34 and beta​ = 0.42, then a​ 1% increase in inputs results in a​ ________ change in output. A. ​0.76% B. ​0.8% C. ​0.76% D. ​8%

Answer 1

Answer:

0.76%

Explanation:

Firstly we write out the production function to be

Y = K^0.34L^0.42.

So if we have inputs that are increased by 1%, we will now have a new production function which is

Y = (K + 0.01 of K)^0.34 (L + 0.01 of L)^0.42

We write this in terms of growth rate

The Growth rate of Y = 0.34 x the growth rate of K + 0.42 x the growth rate of L

This gives us the Growth rate of Y = 0.34 x 1% + 0.42 x 1%

= 0.34+0.42

= 0.76%