1. ## derivatives

Any help would be HUGELY helpful!!!

Assume the demand for a product q1 is a function of its own price (p1) and another product’s price (p2):

q1 = 10p1^-1p2^0.5

(a) Calculate the partial derivatives of the function for both prices.
(b) Using the result obtained in part (a), calculate the own price elasticity of demand.
(c) At what value of p1 is the own price elasticity unit elastic?
(d) Calculate the cross-price elasticity of demand. Is the other good a complement or a substitute? How can you tell?

2. $q_{1} = 10\frac{\sqrt{p_{2}}}{p_{1}}$ ??

Can you do the partial derivatives? Please demonstrate.

Do you have a definition of "Own-Price Elasticity of Demand"? I suspect it has something to do with the p1-partial derivative?

Do you have a definition of "Unit Elastic"?

Do you have a definition of "Cross-Price Elasticity of Demand"? I suspect it has something to do with the p2-partial derivative?

Let's see where you are...

3. Originally Posted by TKHunny
$q1 = 10\frac{\sqrt{p2}}{p1}$ ??

Can you do the partial derivatives? Please demonstrate.

Do you have a definition of "Own-Price Elasticity of Demand"? I suspect it has something to do with the p1-partial derivative?

Do you have a definition of "Unit Elastic"?

Do you have a definition of "Cross-Price Elasticity of Demand"? I suspect it has something to do with the p2-partial derivative?

Let's see where you are...

I really cannot do the partial derivatives, I always seem to get myself in a serious mess.

The "own-price elasticity of demand does relate to the partial derivate of p1 but, like I said before, I just can't get my head around partial derivatives.

Unit elastic is when the elasticity is equal to one, so for the elasticity of demand for an example, the expenditure remains constant as the price changes. I understand that

To be honest I don't fully understand the cross price elasticity of demand but I think it is in relation to the relationship between p1 and p2.

To be perfectly honest I don't fully understand much of this and am seriously stuggling!
I hope you are able to help me in some way, shape or form.

Given $f(x) = \frac{10}{x}$, can you find the first derivative, $f'(x)$?
Given $g(x) = 5\sqrt{x}$, can you find the first derivative, $g'(x)$?