Production Function (Partial Derivatives)
1. Consider the production function f(x,y) = 60x^3/4 y^1/4 ,which gives the number of units of goods produced when utilizing x units of labor and y units of capital.
(a) Compute ∂f/∂x and ∂f/∂y . These quantities are referred to as the ∂x/∂y
marginal productivities of labor and of capital respectively.
(b) If the amount of capital is held fixed at y = 16 and the amount of labor increases by 1 unit, estimate the increase in the quantity of goods produced.
I did part a. And the partial derivatives i got were
∂f/∂x = 45x ^ -1/4 y ^ 1/4
∂f/∂y = 15 x^ 3/4 y ^ -3/4
I got confused with part B. I know that the capital stays at y = 16 but labor increases by 1 which means x= x+1
And I use the partial derivative rule = delta P = P capital (delta capital) + P labor (delta labor)
The capital stays constant so delta capital should be 0...??
Some help would be great!
Re: Production Function (Partial Derivatives)