Suppose k = y¹/²,total factor productivity is constant and equal to 1,s = 0.40,and d = 0.10.When the economy reaches the steady state,investment per worker is ________.

Question

Quizplus · Accepted Answer

In the steady state, investment per worker (i) is given by: 
i = s*y
Using the Cobb-Douglas production function y = k^(1/2) and substituting d and TFP = 1: 
i = 0.40*(k^(1/2)) = 0.40*(y^(1/4)) 
Substituting k = y^(1/2) yields: 
i = 0.40*(y^(1/4))*(y^(1/4)) = 0.40*y^(1/2) 
Because we are in the steady state, investment per worker equals depreciation per worker: 
i = d*y 
Substituting d = 0.10 and solving for y: 
0.40*y^(1/2) = 0.10*y 
y = 6.4 
Finally, substituting y back into our expression for investment per worker: 
i = 0.40*y^(1/2) = 1.6

Suppose K = Y¹/²,total Factor Productivity Is Constant and Equal