Answers/Hints/Solutions DSE 2004-2008: Macroeconomics

For Macroeconomics, since there are lot of diagrams and graphs, which could not be formatted here properly, if anyone want the solutions for the same, can mail us at ecopoint.dse@gmail.com

Contact us : Nishant Mehra (9999886629) and Vidhi Pant (9873903314)

Register here

Answers/Solutions/Hints for DSE 2004-2008: Mathematics/Statistics Part

Utmost care has been taken to provide correct solutions but there can be mistakes so use this document AYOR. In case of mistakes kindly mail us at ecopoint.dse@gmail.com

DSE 2004 Mathematics/Statistics

ECOPOINT : MA Economics 2009 Entrance Coaching by DSE Alumni. 9999886629, 9873903314, 9899048237

Ans 1 (b) only proposition (i) is true (prove using contradiction: if possible $ x Î BÇC, then x Î B and x Î CÞ ? )

Ans 2 (b) there exists a solar system in the milky way galaxy such that every planet in it has a moon revolving around it without any life forms.[negate the given statement]

Ans 26. (c) 2/3 [use baye’s theorem] Ans 27. (d) 3/32 Ans 28. (a) 2/3 Ans 29. (c ) 7.4

Ans 30. (d) 2p²

Part 2

Ans 2 A (a) np(1-p)(p^n-2 + (1-p)^n-2)

A (b) [1-np(1-p) (p^n-2 + (1-p)^n-2)]^k-1 [np(1-p) (p^n-2 + (1-p)^n-2)]

Ans 2 B (a) a=1/48 [ use property of a pdf]

B (b) prob(3 <X <5) = 7/24 [ use ₃ò⁵ a(x-3)dx ]

B (c ) prob (X³ 4) = ¾

DSE 2005 Mathematics/Statistics

ECOPOINT : MA Economics 2009 Entrance Coaching by DSE Alumni. 9999886629, 9873903314, 9899048237

Ans 5 (b) a tribe Ans 6 (d) a tribe

Ans 7 (b) there are atleast two sets of individuals that are both a Club and a Tribe

Ans 8 (a) a club

Ans 13 (d) every book by Bourbaki contains a chapter such that the validity of all the theorems in it is independent of the reader’s gender. [ negate the statement]

Ans 16 (a) P(E È F) = P ( Number of Heads > number of Tails or number of Tails > number of Heads) = 5/8

Ans 17 (b) 2/9 Ans 18 (b) ½ Ans 19 (c) 2p² Ans 20 Do yourself

Ans 21 (b) [ _i=1Sⁿ (c-x_i ) - ₌₁Sⁿ (cy_i - x_i )]/ c Ans 22 (c) 48/65 Ans 23 (c) 3

Part 2

Ans 1 A (a) required variance= 25/49 + 36/49 = 61/49

Ans 1 A (b) required variance= 50

Ans 1 A (c) Null hypothesis H₀ : m_A - m_B =0

Z= [mean(X_A) – mean(X_B)] / Ö [25/36 + 36/49] = -25/1.2 ~ -20

Null hypothesis H₀ is rejected

Ans 1 B (a) True

Ans 1 B (b) True

Ans 1 B (c) False

Ans 1 B (d) False

Ans 1 B (e) True

Ans 4 A Homogenous functions; Euler’s theorem.. prove!!!

Ans 4 B (a) a₃₃ ¹ -3

Ans 4 B (b) Price = 61/6

DSE 2006 Mathematics/Statistics

ECOPOINT : MA Economics 2009 Entrance Coaching by DSE Alumni. 9999886629, 9873903314, 9899048237

Ans 9 (d) 3/8 Ans 12 Do yourself Ans 14 (d) any of the above three conditions is satisfied

Ans 15 (c) f is quasi convex Ans 16 (b) changes the sign of the determinant

Ans 17 should be 1/25 [ 5(1/5x 1/5x 1/5) = 5/125 =1/25 ] Ans 18 (d) 0.82

Ans 27 (c) Rs. 4000 Ans 28 (b) 0.56

Ans 31 (a) 5/14 Ans 32 (d) 2/7 Ans 33 (b) 0 Ans 34 (b) 128

Ans 37 (c) the line defined by y=x+2 and the vertical axis

Ans 46 (d) 7/15 Ans 47 (b) 121/256 Ans 48 (c) 4/13 Ans 49 (a) 28/30

Ans 52 (c) is greater than or equal to 0 at every xÎ Â

Ans 53 (d) in every election, every party has atleast one dishonest candidate. [ negate the statement]

Ans 54 (b) a gang Ans 54 (d) a gang

Ans 56 (b) there are atleast two sets of individuals that are both a family and a gang

Ans 57 (a) a family

Ans 58 (a) 45 Ans 59 (b) 3/8 Ans 60 (d) f(x) =|x| where xÎÂ and x ³0

DSE 2007 Mathematics/Statistics

ECOPOINT : MA Economics 2009 Entrance Coaching by DSE Alumni. 9999886629, 9873903314, 9899048237

Ans 11 (a) f(x) = x²

Ans 12 (c) det A = det B [ by operations on determinant]

Ans 13 (b) Df(x)=0 for some xÎ Â

Ans 14 (d) in every legislature and every party, there exists a legislature who doesnot pay taxes

Ans 15 (c) singular Ans 16 Do yourself Ans 17 (c) increases steadily from 0 to 1

Ans 18 (d) 4/7 Ans 19 (b) (i)28/30 (ii) 0.29 Ans 20 (c) 7.5 Ans 23 (a) (i) 1 km and (ii) Rs. 100

Ans 41 (a) { (x,r) Âⁿ X Â| f(x)£ r } is convex Ans 42 (a) 2xe^(x2) - e^x

Ans 43 (d) converges neither to 1 nor to -1 Ans 44 (d) [-1,1] Ans 45 (c) (-1,1) Ans 46 (d) d(x,z) £ d(x,y) + d(y,z) Ans 47 (b) (A-B) X C = (AXC) – (BXC) Ans 48 (c) attains a saddle point

Ans 49 (c) 4.5 Ans 50 (d) during warm weather, my crops suffer from pests more than during cooler weather. Therefore, a warm environment must help pests to multiply.

Ans 51 (d) None of the above Ans 52 (3!3!)/6! (option not available) Ans 53 (b) 5/18

Ans 54 (b) (1/2, 3/4, 1/2) Ans 55 (b) 37.6 years Ans 56 (a) 0.025 Ans 57 (d) 5, 0.5, 39

Ans 58 (d) 0.79

Ans 59 (b) there is a significant difference in the performance of the classes at the 5% level but no significant difference at 1% level of significance

Ans 60 (b) there is no significant difference between the districts and the candidate is preferred in district A.

DSE 2008 Mathematics/Statistics

ECOPOINT : MA Economics 2009 Entrance Coaching by DSE Alumni. 9999886629, 9873903314, 9899048237

Ans 1 Do yourself Ans 2 (a) Ans 3 (d)

Ans 4 (c) III and IV [ consider any example based on the respective definitions of mutually exclusive sets and independent sets ]

Ans 5 (a) g(y) = f(Öy) " y= 1,4…..400 and g(y) = 0 otherwise

Ans 16 (a) both functions are linear

Ans 17 (b) -(yx^y-1 + z^x ln z)/ (xz^x-1 + y^z ln y) [ partially derivate, revise differentiation!! ]

Ans 18 (c) constant [ this is simple!!!] Ans 19 (a) will change the sign of det A (true for all nxn matrices ) Ans 20 (b) 3 ( think logically ) Ans 21 (b) Ans 22 (c) Ans 23 (a) Ans 24 (c) Ans 25 (c)

Ans 26 Do yourself Ans 27 Do yourself Ans 28 (d) Ans 29 (b) Ans 30 (c)

Ans 51 (d) the rows of A are linearly independent Ans 52 (a) strictly convex Ans 53 (c) exactly one solution Ans 54 (b) if player 1 plays appropriately, she can win regardless of how 2 actually plays

Ans 55 (a) Ans 56 do yourself!! Ans 57 (b) a set having a single point Ans 58 (a) e^p

Ans 59 (c) is discontinuous at x=0 Ans 60 (c) linearly dependent

Contact us : Nishant Mehra (9999886629) and Vidhi Pant (9873903314)

Register here

Microeconomics 2008 paper: Answers/Hints/Solutions to Past year paper/Exam of Delhi School Of Economics (DSE)

This is the fifth series in solutions to Microeconomics questions asked in DSE Past years papers

Microeconomics 2008

Ans 6. (b) U(x,y) = 10{x²+4xy+4y²}=10{x+2y}² +20

Ans 7. U = min{x+y,2y} Because x=y=3, so consumer chooses on x+y so Px=Py(Think about the missing links here)

Ans 8 (c ) Ans 9 (d) Ans 10 (d) Apply the formula of elasticity of subsitution

Ans 31 (a) (Whole box would be PE. Is it?)

Ans 32 (d) Ans 33 (b) Ans 34 (c) Ans 35 (c)

Ans 36. (a) xR*y, yR*z,zR*x. Cyclical Preferences so WARP is violated

Ans 37 (c ) Derive k=5/1+(5-e)² and e=(10/F)^1/2

Ans 38 (d) Derive 2k²e+2eF²=10k² or e=5k²/F²+k²

Ans 39 (c ) Derive dπ/de=2k2(5-e)-t=0 or t=10k²+F²/k²+F²

Ans 40 Do yourself

Contact us : Nishant Mehra (9999886629) and Vidhi Pant (9873903314)

Register here

Microeconomics 2007 Paper: Answers/Hints/Solutions to past year papers/Exam of Delhi School of Economics (DSE)

This is the fourth series of solutions for Microeconomics questions asked in DSE Past years papers

Microeconomics 2007

Ans 1. (c) {20,0}

Ans 2. (a) a vertical line

Ans 3 (b) K=3/2L

Ans 4. (c) MR < 0 in such a case.(Apply the formula, MR=P(1+1/ed) )

Ans 5 (a) A,B (Applying WARP)

Ans 8 (a) always reduce borrowing

Ans 21 (c) 1200-488L+72L² -4L³

Ans 22 (d) (i) Rs 4,80,000 (Apply πox+(1-π)oy) and (ii) risk loving

Ans 23 (a) (i) 1km and (ii) Rs 100

Ans 24 (a) some firms will exit the industry but other will remain (At P=ATC, Supply > Demand, so?)

Ans 25 (b) 9 Apples

Ans 26 (a) 3.5 kg (SE = 33.5-30=3.5)

Ans 27 (d) ((0,0),( 8^1/2,2),(3-8^1/2,1)) (After maximization exercise, y1=x1/2^1/2,so?)

Ans 28 (c) Pareto efficient because there is a bound on Agent’s 1 ability to consume

Ans 29 (b) 2^1/2 (Hint : a=2y1/x1)

Ans 30. (b) ((0,0),( 3-48^1/2/5, 3-12^1/2/5), ( 48^1/2/5, 12^1/2/5))

Ans 37 (c) (1+δ)w2>(1+r)w1

Ans 38 (a) goes up

Contact us : Nishant Mehra (9999886629), Suresh Kumar (9899048237) and Vidhi Pant (9873903314)

www.ecopoint.in

Microeconomics 2006 Paper: Answers/Hints/Solutions to Past year Papers/Exam of Delhi School of Economics (DSE)

This is the third series in solutions to Microeconomics problems asked in DSE Past years papers

Microeconomics 2006

Ans 1 (b) Pareto efficient. Since both prefer more to less, if you take any chocolates from A and give it to B, then you would make B better off and A worse off, so PE.

Ans 2 (d) all of the above

Ans 3 (b) a private good

Ans 4 (b) Monopsony

Ans 5 (d) C = Q(wr)^1/2

Ans 10 (d) Do yourself

Ans 11 (b) Quasilinear Utility function. (Income elasticity of good x is zero)

Ans 13 (c) remains constant. ( Think what will happen if you have CRS and IRS)

Ans 21. (b) Not a competitive equilibrium allocation but is Pareto efficient. (x1,y1) =(3,3) & (x2,y2)= (7,2). Here PE allocations would be a band of PE Allocations. Find demand functions of agent 1 and 2, for both goods, you will get an equation, where what value you should keep for p1 to equate demand and supply

Ans 22. (a) A competitive equilibrium allocation and is Pareto efficient. (x1,y1) =(10,5) & (x2,y2)= (0,0).

Ans 23 (b) {p1,p2} = {0,1}

Ans 29 (b) {q1,q2}={2,2} (MR1=MC, MR2=MC}

Ans 30 (b) A has x=2,y=0 and B has x=0 and y=2 (Generally, where does PE Allocation of max{x,y} lies? What if you have max{x,2y} or max{2x,y}?)

Ans 40 (b) {x,y} = {2/18,5/18}

Ans 41 (c) x1 increases and x2 decreases

Ans 42 (c) {x1,x2} = {15,7}

Contact us : Nishant Mehra (9999886629) and Vidhi Pant (9873903314)

Register here

Microeconomics 2005 Paper: Answers/Hints/Solutions to Past Years Papers/Exam of Delhi School of Economics (DSE)

This is the second series of Microeconomics Questions asked in DSE

Microeconomics 2005

Ans 1 (d) (x1,y1) =(100,100) & (x2,y2)= (50,0) (Think, can this be a case of multiple competitive equilibrium?) (Here first two could be easily eliminated, but what about (c ) )

Ans 2 (a) (x1,y1) =(50,50) & (x2,y2)= (100,50) (What would be the pareto efficient points, will it be a diagonal line, a line from lower left origin to {100,100} point, or the portion of horizontal part of upper axis. Think!)

Ans 3 ( c) (Think why not b)

Ans 4 (b) (x1,y1) =(50,50) & (x2,y2)= (100,50) (Find out demand functions of agent 1 and 2, for both goods. D1 = {50,50}, D2: x2 Є {0,100}, y2 Є {0,100})

Ans 9 (a) {q1,q2} = {a/3b,a-3/3b}

Ans 10.(a) The market share of more efficient firm increases

Ans 11 (c ) q1 will increase and q2 will decrease. (What is this kind of market model called? {q1,q2} = {(a-ab-2b-1)/2b², (3ab-2b-a+1)/4b²} )

Ans 12. (d) Produce nothing in Plant 2

Contact us : Nishant Mehra (9999886629) and Vidhi Pant (9873903314)

Register here

Microeconomics 2004 Paper: Answers/Hints/solutions to Past Year Papers/Exam of Delhi School of Economics (DSE)

Here I am giving indicative solutions for DSE Papers. I am giving hints and some thought points to ponder over. All mistakes are mine, kindly mail me wherever you find mistakes at ecopoint.dse@gmail.com First I am posting for Micro and in subsequent posts would do for Macro and Maths

Microeconomics 2004

Ans 3.(c) x1=y1 for x1 Є {0,1000} (The set of allocations would be on the diagonal line (Think, what if the Edgeworth box is not a square)

Ans 4. (c) x1=y1 for x1 Є {0,1000} (It is a case of multiple equilibria. Solve for demand functions of i, j (Think, does min-min always give multiple equilibria)

Ans 5 (d) Both are pareto efficient. For both α and β, check by transferring the resources, can you make one person better off and other person worse off. In this case both α and β are pareto efficient.(Remember it is not a square now)

Ans 6 (b) (Again a case of multiple equilibria)

Ans 7. (a) Competitive Equilibrium prices (1,0) .(Think, a good in excess supply is x2. Is this the case always?)

Ans 8. (c ) {q1,q2} = {3-4c/6,c/3}; {s1,s2} = {3-4c/3-2c,2c/3-2c}

Ans 9 (b) No, collusion could be Pareto efficient

Ans 10. (a) ½

Ans 11. (d) Produce nothing in Plant 1

Ans 12. (c ) p=1-q π=(1-q)q-1/2q Find dπ/dq, q=1/4

Ans 13. (a) Use Slutsky SE, {x0,y0} = {5,5/3}, {x1,y1} = {5/2,5/3}, (x1-x0,y1-y0} = {-5/2,0}

Ans14 (d) (200)^1/2 -10.Use Hicksian SE, keeping the original utility constant

Ans 15 (b) At U=25/3. Calculate m =(200)^{1/2. {x1,y1} = {(200)1/2 /4, (200)1/2/6} Δ = {5/2-(200)1/2 /4, 5/3-(200)1/2/6} =(10-(200)1/2 )/4, (10-(200)1/2)/6}

Ans 16. (a) Deficit decreases by 15-(200)^1/2

Ans 17 (d) removing the water subsidy and providing lumpsum subsidy

Contact us : Nishant Mehra (9999886629) and Vidhi Pant (9873903314)

Register here

Analysis of ISI Paper 2004.

MS(QE) of Indian Statistical Institute is one of the most prestigious course in Economics Arena. The course is highly mathematical, and that is its beauty. The entrance exam for ISI, MS(QE) also is highly mathematically intensive but interseting and challenging enough.

We are the group of DSE Alumni, giving coaching for MA Economics Entrance for DSE, ISI and JNU. Here in series of posts to follow, we would be analyzing the past exams. These are only indicative hints, not even solutions to the questions. For further clarifications you can call us at the numbers mentioned below.

Here, we would discuss in brief what has been asked in ISI Past years' papers. I am only analyzing 'Economics' part of the paper right now, for 'Mathematics' part, discussion would be done later on taking all the years together.For some questions I would write "dont dare to ask", since they would be very very easy to solve.

Before the analysis, some piece of advice.

Good thing about ISI is, that they never ask you anything beyond what they have defined as their syllabus. The level of questions is higher no doubt, but doable.

My advice to all the aspirants is, please dont loose hope. If you, while doing the paper, are not able to solve something, some concept goes out of the mind, then even dont panic and do something. They want to know your line of thinking, your economic intution.

Dont sit with an attitude that this paper is bigger than life !

Just sit for complete time there, apply your mind, forget about the results, beware of the games which mind plays with you, just crack the paper there itself, with full concentration,

Write whatever comes to your mind as a logical solution to a problem, dont give up at all.

ISI professors (Gods), want to judge your mental stamina, how much you can think. Believe me all of you, have a chance to win, just dont give up before the bell rings..


ISI 2004-Economics Part (http://www.isical.ac.in/~deanweb/syllsqmsqe2k4(mod).pdf) Copy it

Ques 1. Part 1. Very simple. Find out optimal bundle in Perfect subsitutes and apply formula for own price elasticity.

Part 2. Form two equations and find out x

Part 3. Production function in min form then cost function would be in Perfect subsitutes form

Part 4. Dont dare to ask !!

Part 5. Derivate the C + I + G =Y equation and get the solution

Part 6. XII Class level question


Ques 2. Part 1 & 2, Dont dare to ask

Part 3. Apply the definition of homethetic prefernces in all kinds of utility functions and then see


Ques 3. One of the firm will go out of market because of incidence of fixed cost. Find out


Ques 4. Simple Macro

Ques 5. Part 1. Budget line: Xe^2 + Xo = 2(I-R)

Part 2. {Xe,Xo} = {1,1/2}

Part 3. I - 1/2 -Xo

Ques 6. Even if income incraeses then consumption will not incraese after a certain point. Why?

Ques 7. They have told you what Laffer curve is and how it is drawn. Just use Implicit Function, to solve this

You can call us for further clarifications. All the best !!

Registration starts for Daily batches on 4th May or 21st May !! Register yourself fast before seats fill up.


Contact us : Nishant Mehra (9999886629) and Vidhi Pant (9873903314)

Register here