You are given the production function Y=F(K,L)=K1/3L2/3 . a. Convert the product

Question

You are given the production function Y=F(K,L)=K1/3L2/3 . a. Convert the production function to a function relating Y/L to K/L. b. Consider two countries that have access to the same technology, the same quantity of labor and capital, the same production function given above, and capital depreciates at the same rate. Over a long period of time, suppose that one country has per-worker output 10 times more than the other country. Where does this difference come from? Quantitatively explain it using appropriate equations.

Explanation / Answer

Y=F(k,L) = k/3 x2La/3

3Y=2kla

Y=2/3KLa

If 30 Y=2kLa

Y= 1/15KLa -----1

Y= 2/3 KLa -------2 (Divide)

1=1/15 / 2/3

Hence, 1= 1/10 Hence 10 times more capital is needed

Hence proved

By,

Nishant Bhatt

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