Question

Evaluate MPK and MPL for the production function

Q=2LK+ L
given that the current levels of K and L are 7 and 4, respectively. Hence

(a) write down the value of MRTS

(b) estimate the increase in capital needed to maintain the current level of output given

a 1 unit decrease in labour.

Answer 1

The production function is given as

Q= 2LK +L.......(i)

Therefore, Marginal productivity of capital or MPK

is dQ/dK = 2L= 2.4=8 (Taking partial derivative of (i) w.r.t. K)

Also Marginal productivity of labour or MPL is

dQ/dL= K+1 = 7+1=8 (Taking partial derivative of (i) w.r.t. L)

a) MRTS or marginal rate of technical substitution = MPK/MPL=8/8=1

b) Total output is Q= 2LK+L =2*7*4+4 = 60

If L is decreased by 1 then L = 4-1=3

Then Q=2LK+L or, 60=2*3K+3 ( Since total output remains the same under the new condition)

or 6K=60-3=57 or, K=19/2=9.5

Therefore, the increase in K = 9.5-7= 2.5