Assume that a production function is given by y = AK^1/3 L^2/3. If A = 6 and L = 1, the depreciation rate is 0.15

Assume that a production function is given by y = AK^1/3 L^2/3. If A = 6 and L = 1, the depreciation rate is 0.15, and the savings rate is 0.4, the steady-state level of capital is?

Expert Solution

Putting the value of L=1 and A=6 in the production function we get :

y=6K^1/2

Investment function= sy

=0.4*6K^1/2.......... (1)

Depreciation= depreciation rate* capital stock

=0.15*K .............(2)

At steady state equation (1)=(2)

Therefore, 2.4K^1/2 = 0.15K

Or, 2.4/0.15=K^1/2

Or, K^1/2= 16

Or, K= 256. ( Ans)

Rahul Sunny answered 2 years ago

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