D.S.E paper 2005,question no. 15

[Rishita]

consider Ms. Bijlee ,whose utility function is min(E,W),where E is her electricity consumption and W is her consumption of widgets.Suppose Ms. Bijlee's income isRs. 10 and price of eletricity is 1 and  price of widgets is 1.In order to curb Ms. Bijlee's electricity consumption the electricity company decides to impose a surcharge of rs.1 on every unit of electricity consumed in excess of 4 units.What is the resulting reduction in  Ms. Bijlee's electricity consumption ?
a.1/4  
b.1/5
c.1/3
d.1/6
sir i am not getting any of the options as my answer,i am explaining what i have done below.
u=min(e,W)
Budget line E+W=10 for E<4 and E=4 , 2E+W=10 for E>4 from here we are getting E=10/3, before surcharge E=5,so reduction=5/3.

[duck]

Hello Rishita :)

The answer is 1/3

When there was no surcharge, they consumed E=W= 5 units

Now,
>For first four units, the budget line is E+W=8
=> E=W=4
while after four units, it will be> 2E+W=2
=> E=W= 2/3
Therefore,
 E=4+2/3= 14/3
and W=4+2/3=14/3

Hence, the change= 5-14/3 = 1/3

You have basically taken the price of E to be rs 2 for every unit of E but the ques says imposing a surcharge of rs.1 on every unit of electricity consumed in excess of 4 units

:)

[Rishita Saha]

Sir ,
Please give me the solution of the problem
Consider an economy with the aggregate production function Y= alphaK+betaL ,where alpha and beta are positive constants , K is capital , L is labour and Y is output . K is fixed in short run . Perfect competitive producers take the nominal wage rate W and the price level P as given , and employ labour so as to maximize profit .This generates the labour demand schedule .The labour supply schedule is
Ls = -gama+ deltaW/P , where gama and delta are positive constants .Producers and workers have perfect information about P and W .
43.The labour market will clear if and only if
a.beta >gama/delta
b.beta<gama/delta
c.beta>delta/gama
d.beta<delta/gama.
this part I have done.Please solve the following part
44.Assume that the required parametric condition of the previous question holds and that the nominal wage rate is fixed .The short run aggregate supply schedule for the economy is , with Palong the vertical axis and Y along the horizontal axis ,will look as follows:
a.for high values of P it will be horizontal ;for some mid-range values of P it will be downward sloping ; for low values of P it will be horizontal again .
b.for high values of P it will be horizontal ;for some mid-range values of P it will be upward sloping ; for low values of P it will be horizontal again .
c.for high values of P it will be vertical ;for some mid-range values of P it will be downward sloping ; for low values of P it will be vertical again .
d.for high values of P it will be vertical ;for some mid-range values of P it will be upward sloping ; for low values of P it will be vertical again
45. If there is a one shot increase in the fixed stock of the capital stock ,then in the short run aggregate supply schedule will
a.shift up
b.shift down
c.shift to the left
d.shift to the right

Ans. from the production function I get W/P=beta.It means labour demand function is horizontal and labour supply surve is upward sloping . But from this I can not under stand how the aggregate supply curve will loke like.Please reply....

[Amit Goyal]

Vary P and solve for the equilibrium level of wage and employment as a function of P. Take this equilibrium employment level as a function of P, put it in the production function to get the total output as a function of P. And thats your aggregate supply.

[Rishita Saha]

Sir,
   I can not understand how to solve the problerm no 14. and 15 of of D.S. E 2004 .Please explain..Please reply....

[Amit Goyal]

Please post the complete question if you want me to answer something.

[Rishita Saha]

Consider a Person who consumes water and bread , deriving utility xy if x is the amount of water is consumed and y is the amount of bread is consumed .Suppose this person's income is Rs.10 ,the unit price of bread is Rs. 3 and the unit price of water is Rs. 1 .The price of water incorporates a per unit subsidy of Rs.1 i.e for every unit of water consumed by the person ,she pays Re.1 to the water supplier .Suppose this person's demand is (x0 , y0 ).

 

13.Suppose the water subsidy is removed and she has to pay Rs.2 for each unit of water . Let (x1 , y1) be the new demand , what is the resulting change in this person's demand i.e (x1-x0 , y1-y0) ?

a.(-5/2 ,0)

b.(-5/2 , 10/9 )

c.(-10/3 , 10/9 )

d.(-10/3 ,0)

 

14.If the Gove provide this person a lumpsum income subsidy that exactly offsets her utility loss on account of removal of the water subsidy , then the required lumpsum subsidy is

a.9/4

b.5/3

c.root(56)+4

d.root(200)-10

 

15. The income effect of the removal of water subsidy is

a.(10+root(200)/4 , 10+root(200)/6 )

b.(10-root200/4 , 10-root(200)/6)

c.(-1/2 , -1/3 )

d.(5-root(200)/4 ,15 -root(200)/6 )

 No.13 I have done.But I can not understand how to solve 14 and 15. Please explain...

 

[PRIYANKA]

hi

demand function for water x = M/2p_x
y= M/p_y

so for ques 13 using these function you should get ans as (-5/2,0)
ques 14 take U* = xy       (i),
where U* is level of utility derived by consuming x and y at price (p_x,P_y) = (1,3). so, find out its value.
now u have to derive that level of income for which u will get same utility at prices (2,3)
use the fact that MRS= price ratio          (ii)
use (i) and (ii)
to find M' = 2x+3y
now calculate difference between M and M'
following these steps u will get ans as 200^1/2-10

ques 15 find out difference between demand at M and prices (2,3)  and demand at M' and prices (2,3)
using this u should get (b) ((10-:200)/4, (10-:200)/6) as your ans

[PRIYANKA]

sorry by mistake i have written
demand function of y = M/P_y
it should be Y= M/2P_y

[Rishita Saha]

Thank u very much....

[Rishita Saha]

An analyst ,using a simple random sample ,obtained a 99%confidence interval for mean monthly family income , y with the following results :Rs. 3200<ybar< Rs .10000.If the analyst had used a 90% confidence interval instead ,then the interval would be :
a.Shorter and would involve a larger risk of being an incorrect interval estmate.
b.longer and would involve a smaller risk of being an incorrect interval estmate.
c.Shorter and would involve a smaller risk of being an incorrect interval estmate.
d.longer and would involve a longer risk of being an incorrect interval estmate.

I think ans. a. is correct. Is it true?? please reply..

[Rishita Saha]

30. The shift in the LM curve as a result of an increase in the money supply is :
a.equal to the increase in the moner supply.
b.exactly proportionate to the increase in the money supply.
c.less than proportionate to the increase in the money supply.
d.More than proportionate to the increase in the money supply.
 

Ans. let m=K(y) +l(r)
          dm=k'dy+l'dr
          let dr=0
          dy/dm=1/k' >1
So ans is d. Is it correct??? please reply..

[Amit Goyal]

Its (a). You are right.

[Amit Goyal]

Lets see what is going on in this problem. Assuming linear LM schedule:
M = ky - hi,  k>0 and h>0
can be rewritten as
y = M/k + hi/k
Clearly if you double the money supply the output less than doubles (at a fixed positive i)
Hence given the information that is provided in the problem, (c) seems to be the most appropriate choice. i.e. shift in the LM curve as a result of an increase in the money supply is less than proportionate to the increase in the money supply.

[bs5.cam786]

hi rishita can u pls tell me that which book has this type of topic and answers, i mean which books has solution of this question if u dont mind i m a new member and starting the self study so i really need help

[Rishita Saha]

For Microeconomics you can follow Hall Varian , Pyndick mainly. For
macroeconomics Mankiew. I think this is enough..

[ritu]

and rishita for maths i am relying on 11,12 rd sharma and 1st year chiang..... its ok??????

[Rishita Saha]

Yes.For Stat u cn follow N.G.Das..

[vikram]

Hello Sir, in this case can you please specify the equilibrium case? I haven't understood how P varies and how it changes the equilibrium employment. The labour demand curve is a horizontal line and varying P doesn't seem to change anything.

[Suneja]

@duck
why did we take the budget constrain for first four units as : budget line is E+W=8
and for after four units, it will be> 2E+W=2

cant it be tis way
for x<= 4 BL: E+W=10
for x>4 BL: 2(E-4) +W= 10-(4*1)
since for x>4, 4 units of x has already been consumed so that so be deducted from x as well as budget constraint

plz chk if tis way is correct and do explain your ans given earlier.