DSE 2006

[Rain Man]

Q . An increase in foreign income _________ the equilibrium output of a small open economy with uncovered interest parity and flexibe exchange rates.
a. increases
b.decreases
c. leaves unchanged
d first increases then decreases

please explain..

thanks

[Chinni18]

An increase in foreign income leaves unchanged the equilibrium output of a small open economy with uncovered interest parity and flexibe exchange rates. This is because increase in foreign income causes the IS curve to shift upwards and to the right, causing interest rates to rise and thus the domestic currency to appreciate. Any rise in income which occurs is thus countered by the fact that capital inflows will cause exports to deteriorate. In fact, this mechanism is the reason why most small open economis prefer flexible exchange rate regimes: it insulates them from foreign originated disturbances.
Refer Mankiw for a detailed explanation

[Chinni18]

Hey can someone explain this question:
Q.26 0f DSE 2006

Aggregate production function in an economy at a time t is Kt= min {Kt/2 , Lt/4}, where Kt and Lt are respectively the aggregate stock of labour at time t.
In each period 20% of the total output is saved and invested, which augments the next period's capital stock. Capital doesn't depreciate. Labor stock grows by 4 units in every time period. Currently the economy has 200 units of capital and 420 units of labour. What is the current level of employment and what will be the level of employment tomorrow?

Answer to this question is Current employment: 400, Employment tomorrow: 424

Can anyone please explain the reasoning behind this?

[sonudelhi]

given Yt=min{Kt/2,Lt/4}

Yt=min{200/2,420/4}=100

also Yt=Kt/2=Lt/4

implies Lt=4Yt=4*100=400 current employment

Kt+1=200 +20% of output is saved and invested
      =200+20=220

Lt+1=420+4=424

Yt+1=min{220/2,424/4}=min{110,106}=106

therefore Lt+1=4Yt=4*106=424 employment tomorrow


hey chinni can you help me in question 21,22,23 0f dSE 2006

[Chinni18]

Thank you for the concise explanation sonu delhi  I see now what I was doing wrong. Thanks!!!

[Chinni18]

For Q 21, 22, 23
We know that total endowment = (10,5)
U1 = min {x1, y1} and U2 = min {x2,y2} are the utility functions for agents 1 and 2 respectively
Setting p1 as the numeraire, we get optimal bundles as:
x1* = y1* = m1 / (1+p2) and x2* = y2* = m2 / (1+p2)

Budget constraints must satisfy
p1. 0 + p2. 5 = m1 and p1.10 + p2. 0 = m2 because (0,5) and (10,0) are initial endowments
=> 5 p2 = m1 and 10 = m2

Total demand for good 1 must add to 10
=> x1* + x2* = 10
=> {m1 / (1+p2)} + {m2 / (1+p2)} = 10
But we have obtained 5 p2 = m1 and 10 = m2
So {5 p2 / (1+p2)} + {10 / (1+p2)} = 10
=> p2 + 2 = 2 + 2 p2
=> p2 = 0
This doesn't make sense because x and y are complementary goods and not in excess supply

Do the process again by normalising p2=1
You get x1* = 5/(1+p1) and x2*=10p1 / (1+p1)
Again x1* + x2* = 10
=> 5 +10p1 + 10p1 = 10
No value of p1 can satisfy this
Look at the market for  y: y1*+y2* = 5
=> 5 +10p1 + 10p1 = 5
=> p1 = 0

With (p1,p2) = (0,1), you get x1*=5, x2*=0, y1*=5, y2*=0
So competitive eqbm allocation is (5,5) and (0,0)

[Chinni18]

Q21
Examine (x1,y1)=(3,3) and x2,y2)=(7,2)
In market for x we need 3p1+3p2=5p2
We know p1=0 => 3p2 = 5p2 => No value of p2 satisfies this
So its not a competitive equilibrium.
But it is pareto efficient because you cannot make either of the agents better off without making the other one worse off.
Thus option (b)

[Chinni18]

Q 22
Examine it the same way as Q 21
With p1=0 and p2=1, we need
10p1 + 5p2 = 5p2 and 0 p1 + 0p2 = 10 p1
=> p2=1 and p1=0
It fits, so its a competitive eqbm
It is also P.E.
Thus option (a)

[Chinni18]

Q23
We have already found (p1,p2) = (0,1)

[aditi5000]

Hey did anyone solve question 51 of 2006?
question asks for deadweight welfare loss... is that gross or net... (net is the sum of two small internal triangles next to the govt revenue i think..) but either way, i am not getting any of the options!!... please help.

And also question 52.. it says f is strictly increasing i.e. if x>y then f(x) > f(y) ..so  shouldn't f'(x)  be strictly greater than zero ?? if it is equal to zero then that means the function itself must be a constant function.. (or it could be a critical point...) but a constant function is not strictly increasing or strictly decreasing... so how does this make sense? is this a reference to critical points of inflection where the rate of increase is changing ? from concave to convex or vice versa?
why is it c.. and not d?

Please help.

[sonudelhi]

i think correct answer of 51 is=1/2*t/b+1*t=t2/2(b+1)

[sonudelhi]

hey chini,what is problem with p2=0,what do you mean by(This doesn't make sense because x and y are complementary goods and not in excess supply)........... the same can happen when p1=0

hey plz solve 1,2,3,4 of DSE-2005,

[sonudelhi]

hey chini,what is problem with p2=0,what do you mean by(This doesn't make sense because x and y are complementary goods and not in excess supply)........... the same can happen when p1=0

hey plz solve 1,2,3,4 of DSE-2005,

[sonudelhi]

hey chini,what is problem with p2=0,what do you mean by(This doesn't make sense because x and y are complementary goods and not in excess supply)........... the same can happen when p1=0

hey plz solve 1,2,3,4 of DSE-2005,

[sonudelhi]

hey chini,what is problem with p2=0,what do you mean by(This doesn't make sense because x and y are complementary goods and not in excess supply)........... the same can happen when p1=0

hey plz solve 1,2,3,4 of DSE-2005,

[Chinni18]

Sec A, Q 5
In 8 13 5 15 20 12, the successive differences are +5, -8, +10, +5, -8
So there is as such no clear pattern. I really can't figure it out

[Chinni18]

sonu delhi, when you get p2=20 you can see that there are no possible values of p that will satisfy the equation.Whereas with p1=0 there is no excess demand or supply. Plot it on an edgeworth box and you'll see see that at (0,1) price ratio the allocations are efficient as ell as competitive

[Chinni18]

@ sonu delhi DSE 2005
As usual maximise their utility to get (x1*,y1*)=(100,100) and (x2*,y2*)=(50,0)
We get this by normalising p1=1 and p2>1 because for consumer 2 it is the case of perfect substitutes.
For competitive equilibrium allocation you see that option d gives maximum utility and satisfies our conditions
For pareto efficient, in option a you cannot make anyone better off.
For price ratio we know that p1=1 and p2>1 i.e. p2>p1. Only option c satisfies this condition

[s]

hey chinni your solutions are really helpful and seems your concepts in gen eq are really good..
so i was wondering if u could help me out on this..
question 3 2005 i figured dat p2>p1 but im getting stuck in finding the values. n if u have assumed p1=1 and p2>1 then how is it that you are arriving at (1/3,2/3)..? if you dont mind please give a detailed solution for checking which price pairs are competitive equilibrium prices in this particular problem

[Chinni18]

@ S
Thank you so much  Now that you know that p2>p1, any values that satisfy this condition will suffice as the answer. It could be (1,2), (3/5,2/5) or anything like that.  The option (1/3,2/3) does indeed satisfy the condition so it has to be the right answer.