7 Tools for Comparative Statics Flashcards
What is the total derivative with respect to t in the function Z= f(g(t),h(t)) where x=g(t) and y=h(t)
dz/dt =pdz/pdx x dx/dt + pdz/pdy x dy/dt
Where pd is the partial derivative
How do you find the partial derivative of z with respect to t if z is a function of x and y which are both functions of s and t
The same chain rule formula can be applied except all derivatives are partial to find pdz/pdt and pdz/pds
pdz/pds= pdz/pdx x pdx/pds + pdz/ pdy x pdy/pds
pdz/pdt= pdz/pdx x pdx/pdt + pdz/ pdy x pdy/pdt
What can be used instead of implicit differentiation?
We can derive an equation for the level curve and take the derivative
If F(x,y)=c what is the relationship between x and y
Y is defined implicitly as a function of x so we can write y=f(x)
What is f’(x) equal to in terms of implicit differentiation of F(x,y)
f’(x)= -F’x(x,y)/F’y(x,y)
What does the degree of homogeneity tell us?
What happens to a function when all inputs are scaled up proportionally
When does a production function exhibit constant returns to scale?
When it’s homogeneous of degree 1
When does a production function exhibit increasing returns to scale?
When homogeneity is greater than 1
When does a production function exhibit decreasing returns to scale?
When the homogeneity is less than 1
When is a function homogeneous of degree zero
When scaling up all inputs proportionally causes no change in output
What is Eulers theorem
Ef,x + Ef,y = k
Where k is the degree of homogeneity
