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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).
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