Discussion Problem_(14)

[duck]

Find the demand for "x" and "y" if the utility function of a consumer is given by:
U(x,y) = max{x,y}
Also, Income = M , Price of x = p1 and Price of y = p2.

[Devika]

This is a concave utility function. So the consumer will specialize in consuming just one good.

Right?

[Devika]

The optimal choice is the boundary point.

[Sumit]

If P1<P2 then (M/p1,0)
& If P1>P2 then (0,M/p2)
& If P1=P2 then either (M/p1,0) or (0,M/p2).

[Mauli]

(x,y)(p1,p2,m)
                   = (m/p1,0)          if p1/p2<1
                      (0     ,m/p2)     if p1/p2>1
                  (m/p1,0) or (0,m/p2) if p1/p2=1

[Sumit]

Guys Help me in this...I got the answer but I'm little skeptical about it...
Q.Ms.X spends all her income on chocolates (X) and ice cream (Y).Her utility function is U(x,y)=Min{4x, 2x+y}.Ms.X consumes 15 chocolates & 10 ice creams.The price of a chocolates is Rs.10.Find out her income.

[Devika]

I'm not quite sure of my approach, but here's how I did it.

At 15,10 the minimum utility is 40. Draw the graph. Optimal point occurs at the kink, i.e 2x=y.
So x=10 and y=20.

x*= m/p1+2p2

m= 150+ 10p2. Substitute the relevant values to get p2=5.

Hence the income is 200.

 

[Mauli]

hi sumit :)
is  m = 200 ?

[Mauli]

yes so, its just tht
since u=40 ,
 optimum occurs where p1/p2=2
exctly the way devika explained

[Devika]

Hey guys,
I need your help with something. In the question posted by Sumit, I was able to draw the indifference curve because a numerical value of the utility was given.
But with an edgeworth box, this isn't the case. I'm not able to draw the indifference sets of the two consumers, without a numeric value of the utility, correctly. How do I go about that?

[duck]

Correct Answer guys.. :)

[Sumit]

Hi Guys,
I'm also getting the M=200.
N my approach is as follow:
As we Know, P1/P2=MU1/MU2, n From Utility function At Point where Ms.X consumes x=15, Y=10 I'm getting MU1=2 n MU2=1..Thus we are getting P2=5...But I think there is something wrong with this..


I think correct approach as Devika mention...
 At optimal point 2x=y.....So, d(y)/d(x)=P1/p2
i.e dy/dx=2=p1/p2...P2=5...n M=200..

[Sumit]

@devika: Are you asking for Pareto optimal point of two consumers who's utility functions is same & equal to
u(x,y)=Min{4x,2x+y}????

[Devika]

I'm asking for the general cases. If the two consumers have cobb doughlas preferences, then its easy to compute the contract curve.
I want to know how to construct the edgeworth box and hence determine the contract curve when both are perfect substitutes or when both are PC, or one PC and one PS.

[Sumit]

For Perfect Substitutes Case:

Suppose consumer A n B both have utility function[U(x,y)]=x+y...Now Plot this on edgeworth box as usual like any other question n try to find out at which point(s) IC of A is tangent to IC of B. you will see that complete edgeworth box including boundry points are pareto optimal points..

Similarly try for PC case:
All the point where IC of A is tangent to IC of B will give you contract curve..

For some more questions try the questions posted by Duck on the following page:
http://discussion-forum.2150183.n2.nabble.com/pareto-efficiency-tp7580677p7580693.html...