Question

Hi could you please help me with the following task. Especially part B part A I can calculate myself.

thanks

Task 2 Consider the following production function: Y = F(K, L) = AKO.4L1.0 Calculate the marginal product of labour Does the production function exhibit diminishing marginal product of labour?

Answer 1

Find the first derivative of the function with respect to L (labor), you will get marginal productivity of labor (which is also the slope of the function in the direction of labor). Now differentiate the function again, It will give you how Marginal productivity of labor will behave( Second derivative says whether slope of a function increases or decreases). If second derivative is greater than equal to zero then production function will not exhibit diminishing marginal productivity but If second derivative of production function comes out to be less than zero then it exhibits diminishing marginal productivity of labor.

I am assuming you know how to find calculate MPL as you don't need help for the first one.

Second derivative of a function is simply that same function differentiated twice.

example, y = 2x

1st derivative = dy/dx = d(2x)/dx = 2

2nd derivative = d^2y/dx^2 = 0 ( as derivative of a constant is zero)