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Several Maths Questions

Hi, I'm stuck on some maths questions and mathematical concepts that I need to grasp. Would appreciate you telling me:

a) If z = F(u, v,w) and u = f (x, y), v = e^−x , and w = lny, find an expression for partialdevz/partialdevx and partialdevz/partialdevy. I don't understand the notation in the first clause :confused:

b) If I have a function z, with variables x and y in, how do I find the elasticities with respect to x and y. Do I differentiate it?

c) How do I determine the degree of homogeneity of a function?

d) What is a degree of freedom and how do I find it?

e) How do I know if a curve is concave or convex?

Thank you for telling me what these are :smile:

Reply 1

Intheshadows

Has anyone got an answer to these?

Reply 2

Nancarrow

Intheshadows

a) If z = F(u, v,w) and u = f (x, y), v = e^−x , and w = lny, find an expression for partialdevz/partialdevx and partialdevz/partialdevy. I don't understand the notation in the first clause :confused:

So z is a function of u,v and w;
u is a function of x and y
v is a function of x
w is a function of y

You'll need some variant of the chain rule. I reckon

dz/dx = (dz/du)(du/dx) + (dz/dv)(dv/dx) + (dz/dw)(dw/dx)

where all the d's are actually those curly partial derivative signs.