# Last few doubts before DSE exam!!

9 messages
Open this post in threaded view
|

## Last few doubts before DSE exam!!

 DSE 2011 Q1 Suppose (v1,v2,v3,...vn) is a set of linearly dependent vestors, none zero. c1,c2,c3....cn are all scalars, not all 0 such that c1*v1+c2*v2+....+cn*vn=0. Minimum number of non-zero scalars is (a)1 (b)2 (c)n-1 (d)cbd Should not the answer be dependent on the dimension of each vector? eg. if it is in R^2 then we need 2 to span the whole set, and if it is in R^3 then we need min. 3 to span the whole vector space. Why is the answer 2? Q2 Consider the following 2 games.                  Hawk                                        Hawk   Dove           Enter (-1,1)                       and Enter (-1,1)  (3,3)      Not Enter (0, 6)                      not enter  (0,6)   (0,7) Compute Nash Equi. What is the lesson drawn? DSE 2010 Q1 The sequence (-1)^n(1+1/n), for n being positive integer The answer to this is "has limit points -1 and 1". But the series actually oscillates between -1 and 1. It doesn't really have a limit point. Please explain. q2 Suppose X1 and X2 are real-valued rv with f as their common pdf. Suppose (x1,x2) is a sample generated by these rv. The expectation of the number of observations in the sample that fall within a specified interval [a,b] is: How to approach this question? DSE 2009 In the IS-LM framework with an external sector i.e. the IS equation now includes a net export term, an appreciation of the (real) exchange rate (a) would result in a decrease in equi. value of income (b) would result in decrease in equi. value of income only if LM is vertical (c) would result in decrease in equi. value of income only if Marshell-Lerner condition is satisfied (d) would result in decrease in equi. value of income only if govt. maintains balanced budget DSE 2007 Consider 2 open economies with fixed exchange rates, when exchange rate is unity. Economies are as follows: i=1,2 Ci = c01 + c1i(Yi-Ti) Ii=Ii(bar) Gi = Gi(bar) Ti = ti*Yi Mi = m0i + m1i*Yi We are given values for these parameters. How to approach this question? DSE 2006 q1 Suppose in a country the inverse demand curve for a good is P = a-Q, where a is positive. Mkt supply curve of a competitive domestic industry is P=b*Q, where b is positive. Country can import any amount of same good at exogenously given world price of P*. If govt. imposes tariff of t per unit of imports, deadweight welfare loss is: (a) t(a-P*) (b) a-b(P*+t) (c) t (d) t^2 q2 An increase in foreign income ______ the equilibrium output of a small open economy with uncovered interest parity and flexible exchange rates. (a)increases (b)decreases (c)leaves unchanged (d)first increases, then decreases DSE 2005 Consider an exchange economy, 2 agents and 2 goods. Agent 1's endowment (100,100) and Agent 2's endowment is (50,0). Utility of 1 is to maximize min(x1,y1) and of 2 is to maximize x2+y2. (There are 4 questions in this set, I have a doubt in the 3rd one) An example of a pair of competitive equilibrium prices (p1,p2) is: (a) (1,0) (b) (0,1) (c) (1/3,2/3) (d) (2/3,1/3) I have been able to figure out that p2>p1, but as the utility of one of the agents is kinky, the slope condition doesn't work. How to proceed here? Answer is (c).
Open this post in threaded view
|

## Re: Last few doubts before DSE exam!!

 hey for 2006 tax questn...the answer is nt given in the options..so solve it normally n u'll get it...
Open this post in threaded view
|

## Re: Last few doubts before DSE exam!!

 and 2007 marco questn..take 1 ctys export and 2 cty's import n vice versa...put the values in their respective eqns...solve for Y n r...
Open this post in threaded view
|

## Re: Last few doubts before DSE exam!!

 In reply to this post by vikram the last question: when px,py=0,1 px*x1+py*y1=y1=M1=px*wx1+py*wy1=100py=100 px*x2+py*y2=y2=M2=50px=0 x1+x2=M1/px+py + M2/py=100+0=100 <150 market doesn clear for x y1+y2=M1/px+py + 0=100 market clears for y so 0,1 not eqn price vector. px,py=1/3,2/3 px*x1+py*y1=x1/3+2y1/3=M1=px*wx1+py*wy1=100py=100 px*x2+py*y2=x2/3+2y2/3=M2=50px=50/3 x1+x2=100+M2/px=100+50/3 /1/3 = 150 mrkt clears y1+y2=100+0=100 mrkt clears so 1/3,2/3 is price vector. first question: let n=3..so c1v1+c2v2+c3v3=0 if we let c1=0 then c2v2+c3v3=0 v2= -c3v3/c2 >0  so c2 cant be zero and neither can c3 so minimum no of non zero scalars is 2
Open this post in threaded view
|

## Re: Last few doubts before DSE exam!!

 In reply to this post by vikram Q1 ans is 2 only..... because its a simple theory concept taken from Linear Algebra about Scalar Independence. For a set of vectors to be independent we need to atleast 2 non zero scalar values for which we get zero i.e. : s1 * v1 + s2 * v2=0 rest scalar can be zero....so for dependence same logic goes
Open this post in threaded view
|

## Re: Last few doubts before DSE exam!!

 Thanks to all! The responses have been very helpful. But please can someone answer the rest of them? There's no time left as well.
Open this post in threaded view
|

## Re: Last few doubts before DSE exam!!

 Can someone please help with these queries? I hate to say but some of them are repeats. Never know which one strikes again!