Question

General equilibrium model of production:To work with this model we will use fictitious numbers that make the calculations simple. We are also looking at the economy at a point in time; later we will use the production model as the foundation for a model of growth that looks at change over time.

Production function Y= A K^1/2L^1/2 Labor supply, L = 25 Capital Stock K = 10,000 Total factor productivity, A = 1

Consider three changes in the economy. Evaluate each separately (that is, setting all other exogenous variables back to the original values above).

Change 1: K increases to 10,816

Change 2: A increases to 1.04

Graph Change

Answer 1

Assuming production function being

Y= AK^1/2L^1/2

Given,

L= 25

Capital Stock (K)= 10000

Total factor productivity (A) = 1

Putting all the values in the production function

Y= 1*(10000)^1/2*(25)^1/2

Y= 100* 5= 500

Change 1

Given,

L=25

Capital Stock (K)= 10816

Total factor productivity (A) = 1

Putting all the values in the production function

Y= 1*(10816)^1/2*(25)^1/2

Y= 104*5 = 520

Change 2

Given,

L=25

Capital Stock (K)= 10000

Total factor productivity (A) = 1.04

Putting all the values in the production function

Y= 1.04*(10000)^1/2*(25)^1/2

Y= 1.04*100*5 =520

Note: Graphs of both the changes are given in the following picture