Not that Hard Calculus Problem... I think

Calculus Level 3

This is a typical production function of a country: Y = 2 K 0.5 K^{0.5} L 0.5 L^{0.5} . Where Y = GDP of the country, K = Physical Capital of the Country and L = Physical Labour of the country. In this country Capital and Labour is a 2 to 1 substitution so that 4K = L. Find the total differentiation with respect to labour. Evaluate this derivative when L = 100


The answer is 1.

Edward So by Edward So , 27, Canada

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1 solution

Y = 2 × L 0.5 × 1 2 × L 0.5 = L Y=2 \times L^{0.5} \times {\frac{1}{2}} \times L^{0.5}=L Y ′ ( L ) = 1 Y'(L)=\boxed{1}

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