I don't do much Macroeconomics, but if you have a specific request for a topic maybe I'll do one. Here is an interesting Phillips curve one I made: ruclips.net/video/EM0SYtDGv3w/видео.html
But the optimal bundle doesn't satisfy the budget line If we put optimal bundle in budget line it turns out to be 5.125 which is greater than 4 Can you please explain this part
It doesn't seem like there's any solution where you will actually have a corner solution where you consume only y and no x. Mathematically, it seems like there is only one type of corner solution in this problem, where you consume only x and no y. With any positive prices and income, setting MRS = px/py results in a positive value of x. Am i missing something? As you keep increasing px in your example, you continue to get a positive x value, albeit closer and closer to 0. So there is now way we actually get to the corner. I can see it graphically, but not mathematically. When I graph this quasilinear function on desmos.com the indifference curve becomes nearly parallel with the y-axis, up to 3 decimal places, an then reaches 10. But presumably you could take this value to a closer and closer value to 10- and never actually reach it. This would mean that x is always positive. The way this was taught to me was that you will always consume some of X, but your decision to consume some of Y depends on the amount of income. i.e. MRS = 1/2*SQRT(x) = px/py, and therefore X* = px^2/4py^2 (a positive number, provided px and py are positive). I = px.X + py.Y, so I = px.(py^2/4px^2) + py.Y, and I = py^2/4px + py.Y, Y* = I/py - py/4px (a negative or positive number) So we need for Y > 0 to be am interior solution, otherwise we will just spend all of our money on X, and none on Y, i.e. [m/px,0] Y>0 I/py - py/4px > 0 I > py^2/4px So the problem is solved in the fashion X*,Y* = [px^2/4py^2, I/py - py/4px], if I > py^2/4px and [m/px, 0], otherwise.
You are right, thanks for the comment! I hadn't thought about the math very carefully. but since the MRS is 1/(2sqrt(x)), as z goes toward zero the slope goes to infinity. So, no matter how steep the budget line is, you will always buy some x.
Does the rule that slope of the indifference curve is steeper than the slope of the budget line mean that this is a corner solution for other types of common utility functions as well?
Hmmm. Just to make sure we are on the same page, exactly what rule are you talking about? I generally thing of the rule being that if the solution is not feasible, e.g. involves a negative amount of x or y, that indicates a corner solution where the solution is to spend all money on the good with the positive value. It has been a while since I made this video, but I don't think I know of a "rule" about the relative slopes. Do you mean steeper at the x intercept? If the corner solution were on the y axis, the budget line would be steeper. But in general, any utility function that has indifference curves touching the x or y axis could have a corner solution- bot a Cobb-Douglas cannot.
You have it backwards. Though I think the notation is a bit confusing and backwards myself (don't blame me! ☺). MRSx,y =MUx/MUy, and means "how much y you would be willing to give up to get one more x".
None really... but when I recorded this I was teaching out of Besanko and Braeutigam's Microeconomics. So, this probably relates to one of their end of chapter exercises.
There are two common ways it is taught, this is one of them. Here is a video where I explain how the two methods are really the same thing: ruclips.net/video/O3MFXT7AdPg/видео.html
Please, correct me if I am wrong, but I think I can't actually "solve" it, since I have a function of X expressed in general terms, and I can't obtain a plain 'X' from it. That is because when I equalize the lagragians Multipliers, after setting the first orden conditions, I get f'(x)=px/py. The following step would be obtaining X=*something* and replace that in ∂L/∂ λ. But only by knowing what f(x) stands for (for instance Ln(x)), I would be able to solve for x. But still, I think I get the general idea. My only question is: You say that in quasilinear Functions, we obtain parallel indifference curves, with the same slope if X=Xo. Now, Given a Cobb-Douglas function, and a fixed value of X; If I move along the Y axis, do I get a different Slope value for each Indifference curve?
For a cobb-douglas, you will get a different slope if you hold x constant, but change y. Easy way to see this: Let U=sqrt(xy). Then the MRS (slope of indifference curves)=y/x. Hold X=5, and increase Y, the slope goes 1/5, 2/5, 3/5,...
Nope- think about it: You can always replace 1 x for 1 y and get the same utility. root(8+1) = root(7+2)=3. So, these are perfect complements with MRS=1.
Do you know what a Cobb-Douglas looks like? If you don't know, I have a video or two for that... I am a professor, not a do your homework for you service. ☺ You can look elsewhere for that, if you want to.
Good question! 1) If you get a negative solution for X or Y. 2) Another way we might be able to tell is if the slope of the budget line (Px/Py) is either greater than the MRS when Y=0, or less than the MRS when X=0. See if that makes sense to you- if not, let me know, and it might make an interesting video...
Thank you so much for this. Such a good explanation. Thanks for not skipping any of the maths either, it really helps to go through step by step.
I am glad it helped you! Cheers!
Not many people shows how to solve numericals,thanks alot.
You are welcome- if you have any special requests, let me know!
yes sir,if u can post a video about numericals on phillips curve and inflation and stuff,its just nowhere to be found,i'll really appreciate it.
numericals on unemployment,inflation and phillips curve is what i want.
I don't do much Macroeconomics, but if you have a specific request for a topic maybe I'll do one. Here is an interesting Phillips curve one I made: ruclips.net/video/EM0SYtDGv3w/видео.html
Thanx sir,you are really doing it to help people,i really appreciate it.
thank you so much, this helped me in my microeconomics course! btw has anyone told u that u sounded like Iron Man?
That cleared everything up for me, thank you so much.
Thank you so much! Extremely helpful.
Thanks a lot..
But the optimal bundle doesn't satisfy the budget line
If we put optimal bundle in budget line it turns out to be 5.125 which is greater than 4
Can you please explain this part
Thank you so much! This is a great video! :)
It doesn't seem like there's any solution where you will actually have a corner solution where you consume only y and no x. Mathematically, it seems like there is only one type of corner solution in this problem, where you consume only x and no y. With any positive prices and income, setting MRS = px/py results in a positive value of x. Am i missing something? As you keep increasing px in your example, you continue to get a positive x value, albeit closer and closer to 0. So there is now way we actually get to the corner. I can see it graphically, but not mathematically. When I graph this quasilinear function on desmos.com the indifference curve becomes nearly parallel with the y-axis, up to 3 decimal places, an then reaches 10. But presumably you could take this value to a closer and closer value to 10- and never actually reach it. This would mean that x is always positive.
The way this was taught to me was that you will always consume some of X, but your decision to consume some of Y depends on the amount of income.
i.e.
MRS = 1/2*SQRT(x) = px/py, and therefore X* = px^2/4py^2 (a positive number, provided px and py are positive).
I = px.X + py.Y, so
I = px.(py^2/4px^2) + py.Y, and
I = py^2/4px + py.Y,
Y* = I/py - py/4px (a negative or positive number)
So we need for Y > 0 to be am interior solution, otherwise we will just spend all of our money on X, and none on Y, i.e. [m/px,0]
Y>0
I/py - py/4px > 0
I > py^2/4px
So the problem is solved in the fashion
X*,Y* = [px^2/4py^2, I/py - py/4px], if I > py^2/4px
and [m/px, 0], otherwise.
You are right, thanks for the comment! I hadn't thought about the math very carefully. but since the MRS is 1/(2sqrt(x)), as z goes toward zero the slope goes to infinity. So, no matter how steep the budget line is, you will always buy some x.
Does the rule that slope of the indifference curve is steeper than the slope of the budget line mean that this is a corner solution for other types of common utility functions as well?
Hmmm. Just to make sure we are on the same page, exactly what rule are you talking about? I generally thing of the rule being that if the solution is not feasible, e.g. involves a negative amount of x or y, that indicates a corner solution where the solution is to spend all money on the good with the positive value. It has been a while since I made this video, but I don't think I know of a "rule" about the relative slopes. Do you mean steeper at the x intercept? If the corner solution were on the y axis, the budget line would be steeper. But in general, any utility function that has indifference curves touching the x or y axis could have a corner solution- bot a Cobb-Douglas cannot.
Is the marginal utility of x increasing ? Is the marginal ulitity of y diminishing ? And the Marginal Rate of Substitution diminishing ?
Perhaps this will help: ruclips.net/video/vtoo-ikL-g0/видео.html
When we talk about MRSx,y we use UMy/UMx and the other way MRSy,x is equal to UMx/UMy. It´s that correct? Thanks for the response
You have it backwards. Though I think the notation is a bit confusing and backwards myself (don't blame me! ☺). MRSx,y =MUx/MUy, and means "how much y you would be willing to give up to get one more x".
great lecture, sir. may i know what are the book you refers to for the lecture? thanks
None really... but when I recorded this I was teaching out of Besanko and Braeutigam's Microeconomics. So, this probably relates to one of their end of chapter exercises.
Good video. But I don't understand something: why didn't you use the lagrangian method? Thanks.
There are two common ways it is taught, this is one of them. Here is a video where I explain how the two methods are really the same thing: ruclips.net/video/O3MFXT7AdPg/видео.html
Ok, so langrangian method is suitable for quasilinear demands aswell?
leandro8894
Absolutely. Do the problem in this video using Lagrangian for practice, and see what happens.
Please, correct me if I am wrong, but I think I can't actually "solve" it, since I have a function of X expressed in general terms, and I can't obtain a plain 'X' from it. That is because when I equalize the lagragians Multipliers, after setting the first orden conditions, I get f'(x)=px/py. The following step would be obtaining X=*something* and replace that in ∂L/∂ λ. But only by knowing what f(x) stands for (for instance Ln(x)), I would be able to solve for x.
But still, I think I get the general idea. My only question is: You say that in quasilinear Functions, we obtain parallel indifference curves, with the same slope if X=Xo. Now, Given a Cobb-Douglas function, and a fixed value of X; If I move along the Y axis, do I get a different Slope value for each Indifference curve?
For a cobb-douglas, you will get a different slope if you hold x constant, but change y. Easy way to see this: Let U=sqrt(xy). Then the MRS (slope of indifference curves)=y/x. Hold X=5, and increase Y, the slope goes 1/5, 2/5, 3/5,...
I dont get how you made the MRS shouldn`t it be 1/( 2*square root (x) ) ?
Yes, what you have is just another way to write what I have. .5=1/2, and x^.5 =sqrt(x).
Thank you , i`m from germany and we don`t use that type of writing so i was confused
is under root x+y is cobb douglas function
Nope- think about it: You can always replace 1 x for 1 y and get the same utility. root(8+1) = root(7+2)=3. So, these are perfect complements with MRS=1.
What about root X × Y
Root(x*Y) = y^.5*y^.5, so ...
Is it cobb Douglas or not
Do you know what a Cobb-Douglas looks like? If you don't know, I have a video or two for that... I am a professor, not a do your homework for you service. ☺ You can look elsewhere for that, if you want to.
Will quasilinear preferences always give corner solutions, or interior solutions are possible?
In my first example there was an interior solution, so yes, it is possible. Just remember, that a corner solution is impossible with a Cobb-Douglas.
BurkeyAcademy Another question: How do we know when we'll get a corner/interior solution?
Good question! 1) If you get a negative solution for X or Y. 2) Another way we might be able to tell is if the slope of the budget line (Px/Py) is either greater than the MRS when Y=0, or less than the MRS when X=0. See if that makes sense to you- if not, let me know, and it might make an interesting video...
BurkeyAcademy This makes complete sense. Thank you so much!
now i can do my pproblem sets in 32L
wait rly
ya omg
AM,AZING ONG