Need Help w/ Partial Elasticity Problem: sum[i=1,3]El x_i z

[Alex_Of_Darkness]

Hi everyone, does anyone would be able to help me with that one? Don't even know where to start so if you could show me how to solve it it would be fantastic!

it's something like z=((ax1)^d + (bx2)^d + (cx3)^d)^g and a,b, c, d & g and constants.


Calculate \(\displaystyle \displaystyle \sum_{i=1}^{3} El \; xi \; z\)

 

[mmm4444bot]

\(\displaystyle \displaystyle \sum_{i=1}^{3}\)\(\displaystyle El \; xi \; z\)

I do not recognize this notation.

Can you explain the meaning of symbol El ?

 

[Alex_Of_Darkness]

I do not recognize this notation.

Can you explain the meaning of symbol El ?

Partial elasticity of z with respect to xi!

 

[mmm4444bot]

Partial elasticity of z with respect to xi!

Thank you!

I googled it, and it appears to be related to a calculus application in economic and business problems.

I didn't see much in the way of online lessons or lectures; most references are books. I perused some information, but I could not find anything presented in the form of a summation. Instead, there are lots of partial differential equations.

We'll need to wait until a volunteer tutor with experience in this applied method chooses to join the conversation. It's beyond my experience.

 

[JeffM]

In general, point elasticities, which have qualitative meaning in economics, involve the ratio of a derivative at a point to the ratio of the variables at that point but may not be fully determined by that ratio. For example, one important elasticity is the absolute value of such a ratio. There are also arc elasticities, which involve the ratio of the ratio of differences between end points and the ratio of the end points. Without a precise definition of the elasticity used in this formula, I could not even begin to think about the math involved.

 

[Alex_Of_Darkness]

In general, point elasticities, which have qualitative meaning in economics, involve the ratio of a derivative at a point to the ratio of the variables at that point but may not be fully determined by that ratio. For example, one important elasticity is the absolute value of such a ratio. There are also arc elasticities, which involve the ratio of the ratio of differences between end points and the ratio of the end points. Without a precise definition of the elasticity used in this formula, I could not even begin to think about the math involved.

For example we would have: Elxz = x/z ∂z/∂x and Elyz = y/z ∂z/∂y. Also Elxz (or Elyz ) equal to the variation in percentage of z caused by the enhancement of 1% of x while y doesn't change. So I guess that with three variables it would be pretty much the same?

 

[JeffM]

For example we would have: Elxz = x/z ∂z/∂x and Elyz = y/z ∂z/∂y. Also Elxz (or Elyz ) equal to the variation in percentage of z caused by the enhancement of 1% of x while y doesn't change. So I guess that with three variables it would be pretty much the same?

That makes sense to me.

 

[Alex_Of_Darkness]

That makes sense to me.

So in that case I would need to use something like ∂z/∂xi but how do I apply that to x1, x2 and x3. Also it seems to be pretty complicated to do this partial derivative. Anyone would know how to do it?

 

[Deleted member 4993]

z=((ax1)^d + (bx2)^d + (cx3)^d)^g and a,b, c, d & g and constants.

dz/dx₁ = g * [(ax₁)^d + (bx₂)^d + (cx₃)^d]^{(g -1)} * d * a^d * x₁^(d-1)


And continue...... not complicated - just tedious.....