micro-consumer theory

[ritu]

Q1.raman  has convex preferences and dislikes both good x and y......is it possible to draw ic's?if yes explain their direction of increasing utility...

Q2.saumya likes x and dislikes y.if she's served y she will have it to be polite......is it possible to draw ic's?if yes explain their direction of increasing utility.

Q3.aloka always gets twice as much satisfaction from an extra x as she does from an extra y......wot type of preferences are these??(is it cobb douglas????)

Q4.suppose pinki and baby spend their income on x and y...pinki's pref are represented  as U(x,y)=10xy and baby's by U(x,y)=0.20( x square)(y square)...do pinki and baby have same or different pref?????explain...

[Amit Goyal]

A1. Example: Plot ICs for U(x, y) = - x - y or U(x, y) = -(x^2) - (y^2) and do it.
A2. Example: Plot ICs for U(x, y) = x - (y^2) and do it.
A3. U(x, y) = 2x  + y They are perfect substitutes.
A4. Both Pinki and Baby have the same preferences.

[ritu]

sir

in Q3 ,though i am aware of basic difference btwn PS,PC and cobb douglus...but when language is changed i get a bit confused..:the answer wud have been cobb douglus when it wud have been given that "he prefers x twice as much y"?????and it wud have been PC only when both are 'consumed' in fixed ratio??????


And one more thing sir,both pinki and baby have same pref coz they have same powers attached to x and y,ie..1,1 and 2,2..ie equal weights have been attached to x and y....but sir doesnt constant A (10 and .2 in this case) affect pref...??????

thank you sir:)

[Bellatrix]

Dear Ritu,

For the 4th question, Utility is basically used to rank our preferences. So the difference in the constants does not matter because for given few bundles and their preference relation between them, shall be preserved even with this Utility function. Jaise we know (2,1) and (1,2) give the same U= 20, and so the consumer is indifferent between the bundles. Now try with the different utility function, we will get U= .2*4*1= .8 for both bundles. So the relation between them is preserved. (indifference)

For the 3rd question, we measure satisfaction from utility. Now the given question can be translated(mathematically) to: delU/delx  = 2 ( delU/dely) , so MUx/MUy = 2 (is fixed)  So the slope of the ICs is a constant and hence these are Perfect Substitutes. Is this explanation satisfactory? :)

[ritu]

hey bellatrix.......
thanx a lot dear........its absolutely clear now:)))))
just tel me that in Q1,when we draw the ic's,will they lie in third quadrant with utility being maximum when consumer is having bundle (o,o).........as per the examples provided by amit sir...??????
thank u again for clearing doubts

[Bellatrix]

Absolutely :) Because he dislikes both goods, he would rather have lesser and lesser of both.

[Bellatrix]

Absolutely :) Because he dislikes both goods, he would rather have lesser and lesser of both.

[Bellatrix]

oh so sorry, see in the 3rd quad, you take negative values of x and y, so further away from (0,0) gives a higher value of utility.

[Bellatrix]

The commodity space is x>=0 and y>=0 so the ICs will be drawn on the first quadrant, downward sloping and straight. Its just the value of the Utility, z axis shall be negative. And when we slice the function for a z<0, then the print of the IC will be on the  first quadrant. eg. -x -y = -1. So now if you are closer to the origin, you get a higher value of U.

So erase my earlier posts :)

[ritu]

thanx:))))))