Question

1. Given the Cobb Douglas production function: Q = 60L0.3 0.7 (0) (ii) (iii) liv) Calculate the level of output when L = 30 and K = 20 Calculate the level of output when both inputs double Comment on the returns to scale Write an expression for In 2. A firm's turnover in yeart is described by y = 20e What is its turnover in year 0 and in year 4? (ii) After how many years will its turnover have doubled since it started trading? (i) o e 9 Pw O

Answer 1

Answer 1.

(i.)

Q=60L^0.3K^0.7

Putting L=30 and K=20

Q=60*(30)^0.3*(20)^0.7

therefore, Q= 1355.21

(ii.)

When inputs are doubled, L=60, K=40

Q=60*(60)^0.3*(40)^0.7

Q=2710.43

(iii.)

The returns to scale is the change in the proportion of output due to a change in the proportion of input. Here, a unit increase in 'K' will result in increasing returns to scale while a unit increase in 'L' will result in diminishing returns to scale because the degree of 'K' (0.7) is greater than the degree of 'L' (0.3).

(iv.)

Making it logarithmic, expression would be

lnQ = ln60 + 0.3ln (L) + 0.7ln (k)