Econ200 (1 Viewer)

[Kutay]

Hey guys i know this is probably an easy question but i dont understand how this equation works out

The price elasticity of demand for example:

I understand how they get change of Q / Change of p x p over q

BUT how do they get to the next part?

the partial derivative of Q / partial deriv of p x p over q

 

[Kutay]

Also does anyone know an example?

 

[Master E]

Hey guys i know this is probably an easy question but i dont understand how this equation works out

The price elasticity of demand for example:

I understand how they get change of Q / Change of p x p over q

BUT how do they get to the next part?

the partial derivative of Q / partial deriv of p x p over q

change in Q / change in p x p over q is the same thing as partial deriv of Q / partial deriv of p x p over q.

THe triangle sign (delta) has the same meaning as that funny "d"

 

[Kutay]

If the utlity function U(x1,x2) = x1x2 and has a budget line p1x1 = p2x2 = mm then the demand function for x1 is ??


the answer is x1 = m / 2p1



I was wondering how you get that?


Also this question if U(x1,x2) = min(x1,5x2) and p1 = 1, p2 = 2 and m = 140, then the demands for x1 and x2 are 100, 20??


I was wondering how you get that as well??

I know it involves differentiating and sub the numbers in just missed so much as have been away

Any help would be much appreciated

 

[randomguy777]

check page 93 of textbook for proof.
utlity function U(x1,x2) = x1x2 is a cobb douglas utility function.
check if your notes have it, cobb douglas relies on some assumptions i suppose.

x1^a x2^b where 'a' and 'b' are random numbers.
optimal choice for x1 = a/(a+b) * m/p1. in this case a = 1 b= 1.
so 1/2 * m/p1=x1 = m / 2p1

im kinda guessing this anyway:

U(x1,x2) = min(x1,5x2) and p1 = 1, p2 = 2 and m = 140, then the demands for x1 and x2 are 100, 20

this is like leontief function, or perfect complements.

use this formula:

m/(p1+p2).<<<<<<<<<<

so since min(x1,5x2). multiply p1=1 by 5 so 1x 5 =5. swap the numbers around.(this one also confuses me but ask your tutor about the logic of it)
leave p2 =5.
to find x1 keep one of the prices constant and other changed.
sub into formula x2: 140/(5+2) = 20.

p2 = 2.
so p2/5= 0.4.

p2=0.4. just changing the number to maintain the min(x1,5x2 ratio.
in this case p1 = 1

so 140/1+0.4=100.