Solow growth model with technological progress An economy ha

Solow growth model with technological progress. An economy has the following production function (in intensive form): 1. where ~ Y/ AL and k = K/AL (output per effective unit of labor and capital stock per effective unit of labor, respectively).

Solution

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The production function is given by-

y=k^1/2

y= Y/AL and k=K/AL

we have to solve for y considering the following facts-

For developed country-

savings rate = 28%

population growth rate = 1% per year

For less-developed country -

savings rate = 10%

population growth rate = 4% per year

and g= 0.02 and alpha =0.04

solving with the values available-

1) For developed country

g*alpha = 0.02*0.04=0.008

k= 28%/0.008= 0.35

hence y = 0.35^1/2=0.175

2) For less developed nation-

g*alpha = 0.02*0.04=0.008

k= 10%/0.008= 1.25

hence y = 0.35^1/2=0.625

and calculating y from above assuming the steady state we get values by calculating g * alpha and then calculating the value of k for the per unit value of labour consumed to finally arrive at value of y by raising k to ½.