sample questions of ISI ME 2 , 2010

[SONAL]

6 (b)
A utility maximizing consumer with a given money income consumes two
commodities X and Y . He is a price taker in the market for X. For Y
there are two alternatives: (A) He purchases Y from the market being a
price taker, (B) The government supplies a fixed quantity of it through
ration shops free of cost. Is the consumer necessarily better off in case
(B)? Explain your answer with respect to the following cases:
(i) Indifference curves are strictly convex to the origin.
(ii) X and Y are perfect substitutes.
(iii) X and Y are perfect complements.

[priyanka p]

hi sonal,  in q3 (b) first write down the dd fns for business and economy class as p1=a1-b1q1    and   p2=a2-b2q2     now first see for business class, eqauate  MR1=MC  ie   a1-2b1q1 shuld be equal to 50  we gwt q1= (a1-50)/2b1 ------------eqn 1.    Now calculate p1 by pluggin this value in the inverse dd fn u get p1=25 + a1/2---------eqn 2.   We have  pofit maximizing levels of quantity and price ie 1500 and 200 respectvly, use them in eqn 1 and 2 to get values of a1 and b1.  thus u get the dd fn.   similarly for economy class

[priyanka p]

hi vishruti, pls tell the correct approach and answer for dead wt loss in ques 2

[priyanka p]

hi vishruti, for the solow model, i got the following answers.     (a) capital labor ratio, k*=16 y=root k*  = 4 is the rate of growth of output , rate of growth of savings= (0.2)y =0.8  wage  i dont know i guess dy/dl =root k*/2 =2      (b) now, k*=.4/.05=8 there4 new steady state rate of output also doubles   (c)  yes it is different, we can show the fig and explainwhat happens when sk(f) shifts.

[SONAL]

thanx priyanka........cud u also explain hw u solvd Q4
for the solow question
a)K/Y=16,
   rate of growth of output=g=n=.05(nt sure)
    i cudn't solve for rate of growth of savings
    wage rate=MPL.p=(1/2).4.p=2(hav assumd p=1)
b)g=.o5
c)yes its different

[priyanka p]

hi sonal, in the first case when ICs r strictly convex, he is worse off in case the fixed quantity is less than he would have consumed in case (a) or he could b better off as well if he get more....so its actually ambiguous.   in 2nd case he is necessarily betteroff as being perfect substitutes he can get extra of free good y , in 2gthr of consuming x wiith his income spent all. in 3rd case of complements again its ambiguous, if qty is lesser than case (a).......i am not sure of the explanations but i guess answers shuld b this way.

[vishruti]

Answer 8

a) capital labor ratio = 16
    rate of growth of output = 0.05
    rate of growth of savings = 0.05

we calculate it as follows: S = s Y . Now we take log on both sidas and diffrentiate wrt t , we get

dS/dt / S = ds/dt / s + dY/dt / Y

the first term on the RHS = 0 because s is a constant and hence dS/dt / S = dY/dt / Y = 0.05

wage rate is MP L = w = 2

b)the growth rate of output is 0.05

c) it does not change because its independent od savings , remember in solow model savings is "exogenous" and it only leads changess in the level and "not" the growth rates

this can also be checked by the following method:

y = Y/L

take log and diffrentiate wrt t

dy/dt / y = dY/dt / Y - dL/dt / L

now LHS is 0 and hence dY/dt / Y = dL/dt  / L..... always......no matter what is the saving rate in the economy

please note that the above holds for the steady state ( where dy/dt / y = dk/dt / k = 0) as asked in teh question

[SONAL]

thanx vishruti...........

7(d) true/false------The amount of stipends which Indian Statistical Institute pays to its students is a part of GDP.

9(a)     Consider the utility function U(x1, x2) = (x1 − s1)^0.5(x2 − s2)^0.5, where
s1 > 0 and s2 > 0 represent subsistence consumption and x1 >=s1 and
x2 >= s2. Using the standard budget constraint, derive the budget share
functions and demand functions of the utility maximizing consumer. Are
they linear in prices? Justify your answer.

(b)       Suppose that a consumer maximizes U(x1, x2) subject to the budget constraint
p(x1 + x2) <= M where x1 >=0, x2 >= 0, M > 0 and p > 0. Moreover,
assume that the utility function is symmetric, that is U(x1, x2) =
U(x2, x1) for all x1 >= 0 and x2 >= 0. If the solution (x1*, x2*) to the consumer’s
constrained optimization problem exists and is unique, then show
that x1*=x2*.

[benhur]

isi changed its pattern!!not fair to us!!!

[ritu]

Here Y=k^.l^0.5
Take log both sides...nd diff wrt ".t  "....
We get Gy=Gk/2+Gl/2
In steady state. Gk is zero so we get Gy as 0.05/2
=2.5%
Shouldnt this be the answer instead of 5%???

[duck]

Hi Ritu..:)

In steady state, Gk is not zero.Its 0.05

At steady state, K/L=16
So, Y = 4
We know, dk/dt = sY
=> dk/dt = 0.20*4 = .80
therefore, (1/K)(dK/dt)= .80/16 = 0.05

[tim]

hi vishruti cn u temme wats ur answer for rate of capital growth and rate of savings ?

[tim]

hi sonal,
did u get the answer for 9a) and 9b).
i started this questn(9a) using lagrange and got (x2-s2)/(x1-s1) = p1/p2 as one eqtn.
i substituted this in the budget constraint. and afta that i gt stuck. so cn u pls temme where did  go wrong?

Benhur plz tell me how  pA ,pB,qa,qb will solve

[Dheeraj]

 In answer 1 part (a) (ii), I think multiplier in this case should be larger because
                 Y = C + I + G
                 Y = c(1-t)Y + I + tY
    [1-t-c(1-t)]Y = I
    [(1-c) (1-t)]Y = I

so multiplier in this case would be 1/ [(1-c)(1-t) ] Y, which is larger than the usual multiplier 1/ [ 1 - c(1-t) ].

Further in (iii) part dY/dt comes out to be positive.

[Dheeraj]

Ans-5 Someone pls let me know if this is correct

  trade balance is given by  TB = T`+ bP*/P - mY, so trade balance equilibrium will be when TB=0, i.e.
  mY = T` + bP*/P

  Commodity market equilibrium:
   Y = C + I + G + X - M
   Y = C`+ c(1-t)Y + I`-br + G`+ X`- mY    ; here (`) represents (bar) to represent exogenous..Here we assume export as exogenous.

   Y = A`+ c(1-t)Y - br - (T`+ bP*/P)  ; where A`= C`+I`+G`+X` and from TB equilibrium mY = T` + bP*/P

   [ 1-c(1-t) ] Y = A`- br - (T`+ bP*/P)

 (a) this curve will be same as IS curve for closed economy because both represent the negative relation between r and Y. LM curve can be drawn as usual upward sloping on (Y,r) plane.

 (b) Now if government spending is increased this curve would shift rightwards causing an increase in interest rate and income. Now when income increases, imports will increase and trade balance will get worsen. To maintain the trade balance equilibrium, the home currency should depreciate i.e. exchange rate 'e' should increase.
 
 (c) when P* increases, income should decrease from the above equation. and then to maintain the trade balance 'e' should also decrease.

  Let me know if there is something wrong in  this..

[neha 1]

pls explain ques 4

[Dheeraj]

Ans 4:
X1= root(L1*K) ....(1)
X2= root(L2*T) ......(2)
 
MPL1=1/2* root(K/L1)
MPL2=1/2* root(T/L2)

As labor is perfectly mobile between two sectors, the wages will be equal in two sectors.

P1*MPL1 = P2*MPL2 ......(3)

We know K=K' and T=T'. Now divide equation (1) by (2) and find L1/L2 in terms of X1/X2. from this and eqation (3), you can get the relation between X1/X2 and P1/P2.

for part (b), simply plot relative price on Y-axis and relative supply and demand on X-axis. As 'gamma' goes up, relative demand curve shifts rightward for every relative price. So as gamma goes up, in new equilibrium relative price increases.

[niruj]

Plz answer the question 9. b)

[Arpita Banerjee]

Kindly can you explain how you derived the demand curves actually can't make out how you got it , it would be of great help..
This is for part b )