# Implicit Function Theorem

Use the Implicit Function Theorem to derive an equation for the slope of the isoquant associated with this production function.

12. You have the following production function for good X:

where output (Q) is fixed at a specific level, K is the quantity of capital and L is the quantity of labor used to produce good X. The isoquant associated with this function tells us how much capital and labor must be used to produce our given level of output.

a. Use the Implicit Function Theorem to derive an equation for the slope of the isoquant associated with this production function.

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...50(K^0.3)*0.7(L^-0.3)=35(K/L)^0.3

dQ/dK=50*0.3(K^-0.7)*(L^0.7)=15(L/K)^0.7

The implicit ...