6 Functions of Many Variables Flashcards
What do partial derivatives measure
How a function of several variables changes when one of the variables changes
How are all variables except the the one being partially differentiated treated?
As constants
If we have a production function, what does the partial derivative of the function with respect to capital tell us?
The marginal product of capital
What is a second order partial derivative
d^2f/dx^2 is the derivative of df/dx with respect to x when other variables are treated as constants
What is Young’s theorem
If the partial derivatives are continuous the order of differentiation doesn’t matter
What does the second order partial derivative of production with respect to labour tell us
It tells us how the marginal product of labour changes as L changes
What is the equation for the partial elasticity of of z with respect to x
Ez,x= pdz/pdx x x/z = pdln(z)/pdln(x)
