Question

1-Consider the production function ? = ?? ?(?ℎ) ^1−? . Transform the production function into per-worker terms and show how growth in productivity can be estimated, even though it is not directly observable. Show your work

Answer 1

......................................................(1)

Y= Amount of amount produced

A = Technological Progess /Productivity

L_h= Labor employed

Dividing equation(1) by L_h

...................................................(2)

Let us assume the following

is the per capita level of output produced

.

is the per capita level of kapital emloyed

............................................................................(3)

Growth of any variable can be determined by taking log of the above equation(3) as First Difference of Log = percentage change. Logging converts the absolute differences into relative (i.e., percentage) differences. Thus, the percentage change in Y at period t is defined as (Y(t)-Y(t-1))/Y(t-1),which is approximately equal to LOG(Y(t)) - LOG(Y(t-1)),but the approximation is almost exact if the percentage change is small.

..............................(4)

..............................(5)

where,

Growth in Productivity

Growth in per capita output produced

Growth in per capita k employed

Hence, ( equation 5) shows the growth in the productivity.