DSE -Entrance Solutions - Weeblysbcs.weebly.com/uploads/1/1/0/5/1105777/dsesolutions.pdf · DSE -Entrance Solutions Economics This document contains solutions of past year exam problems

DSE-Entrance

Solutions Economics

This document contains solutions of past year exam problems asked in Delhi

School of Economics entrance exams held for admissions to their masters

program(2004-08).

Disclaimer: The solutions offered in the document can be incorrect, the likelihood

of which is very small though, so use at your own risk. The possible reasons for

mistakes could be my ignorance or laziness with former being more likely of the

two.

2010

Amit Kumar Goyal

economicsentrance.weebly.com, beaneconomist.com

2/15/2010

Entrance Exam solutions economicsentrance.weebly.com beaneconomist.com

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Prepared by: Amit Kumar Goyal

DSE: Year 2004

Part - 1

1. (b) only proposition (i) is true 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 3. (c) x1=y1, for x1Є[0,1000] 4. (c) x1=y1, for x1Є[0,1000] 5. (d) both α and β are pareto efficient 6. (b) x1=999 and y1Є[999,1000] 7. (a) (1,0) 8. (c) s1 = (3-4c)/(3-2c) and s2 = 2c/(3-2c) 9. (b) no 10. (a) ½ 11. (d) produce nothing in Plant 1 12. (c) ¼ 13. (a) (-5/2, 0) 14. (d) √200 – 10 15. (b) ((10-√200)/4, (10-√200)/6) 16. (a) deficit decreases by 15-√200 17. (d) removing the water subsidy and providing a lump-sum subsidy. 18. (b) (µβ+α)/P[µ(1-c)+αλ] 19. µ/[µ(1-c)+αλ] 20. (d) Y = f(½) 21. (b) max {W0, P/2} 22. (a) min{½, 1- W0/P} 23. (c) f(½) 24. (c) Y does not decrease and P increases 25. (b) Y does not increase and P decreases 26. (c) 2/3


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27. (d) 3/32 28. (a) 2/3 29. (c) 7.4 30. 2p2

Part – 2

1. (A) Effect of a marginal increase in G on AD: Y = C(Y-T) + I(r) + G, M/P=L(Y, r) Differentiating totally, (1-CY)dY - Irdr = dG LYdY + Lrdr = dM/P Solving, dY/dG = Lr/(Lr(1-CY)+ IrLY) Refer book for explanation (B) Refer book for explanantion

2. (A) (a) np(1-p)(pn-2+(1-p)n-2) (b) (1- np(1-p)(pn-2+(1-p)n-2))k-1 (np(1-p)(pn-2+(1-p)n-2)) (B) (a) a=1/48 (b) 7/24 (c) 3/4

3. (A) f(x1, x2)= x2g(x1/x2) ( BY CRS ) MP1= g’(x1/x2) MP2= g(x1/x2)-(x1/x2) g’(x1/x2) MP11= (1/x2)g”(x1/x2) < 0, (given in (b)) Hence, MP12=- (x1/(x2)2)g”(x1/x2) > 0 Similarly, MP21 > 0. (B) For a33 ‡ 3 Economic interpretation : For a33 ‡ 3, the three securities when combined appropriately can generate any return. (C) To show : f is convex if and only if {(x,r)|f(x)≤r} is convex. Suppose f is convex.


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To show: {(x,r)|f(x)≤r} is convex Let (x1,r1), (x2,r2) belongs to {(x,r)|f(x)≤r} . So, f(x1)≤r1 and f(x2)≤r2 Take 0<t <1, we want to show that f(tx1+(1-t)x2) ≤ tr1+(1-t)r2 By convexity of function, f(tx1+(1-t)x2) ≤ tf(x1)+(1-t)f(x2) ≤ tr1+(1-t)r2. Now suppose {(x,r)|f(x)≤r} is convex To show: f is convex. (x1,f(x1)) and (x2,f(x2)) belongs to {(x,r)|f(x)≤r} . Since the set is convex, (tx1+(1-t)x2, tf(x1)+(1-t)f(x2)) belongs to {(x,r)|f(x)≤r}. This implies f is convex.

4. (A) (a) SC =pxx+(25py)/x. (b) LC =10(pxpy)1/2 (c) x = 5(py/px)1/2

(d) x = (3.5) (2py/px)1/2

(B) Member 1 will veto b. Member 2 will veto d. Member 3 will veto c.


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DSE: Year 2005

Part - 1

1. (d) (x1,y1)=(100,100) and (x2,y2)=(50,0) 2. (a) (x1,y1)=(50,50) and (x2,y2)=(100,50) 3. (c) (1/3, 2/3) 4. (b) (x1,y1)=(50,50) and (x2,y2)=(100,50) 5. (b) a Tribe 6. (d) a Tribe 7. (b) There are at least two sets of individuals that are both a Club and a

Tribe. 8. (a) a Club 9. (a) q1=a/3b and q2=(a-3)/3b

10. (b) The market share of the more efficient firm decreases. 11. (c) q1 will increase and q2 will decrease. 12. (d) produce nothing in plant 2. 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. 14. (c) 11.2 15. (c) 1/3 16. (a) 5/8 17. (b) 2/9 18. (b) 1/2 19. (c) 2p2 20. (a) 2/3 21. (b) n-n(mean(y)) 22. (c) 48/65 23. (c) 3 24. (c) right if the price level falls and/or the quantity of money rises. 25. (d) None of the above choices is correct


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26. (b) one; zero 27. (a) IS curve was vertical and stuck at a low level of income. 28. (c) ½; -½ 29. (b) decreasing; decreasing 30. (a) increasing; increasing

Part – 2

1. (A)(a) Required Variance=25/49+36/49=61/49 (b) Required Variance = 50 (c) Null Hypothesis: H0 = µA-µB=0 Test statistic value: z = (mean(xA)-mean(xB))/√[(25/36)+(36/49)] = -25/1.2 ≈ -20, Null is rejected. (B) (a) True (b) True (c) False (d) False (e) True

2. Given the information we can derive that Aggregate supply curve will be vertical, hence an increase in supply of money will shift AD curve outwards and can only lead to rise in prices without affecting the output.

3. (A) (a) SC =pxx+(25py)/x. (b) LC =10(pxpy)1/2 (c) x = 5(py/px)1/2

(d) x = (3.5) (2py/px)1/2 (B) (q1,q2,q3)=(1/2,1/4,1/8)

4. (A) Refer Textbook (B) (a) a33 ‡ -3; (b) Price = 61/6


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DSE: Year 2006

Part - 1

1. (b) pareto efficient 2. (d) all of the above 3. (b) a private good 4. (b) monopsony 5. (d) C = Q√(wr) 6. (d) complete crowding out and no increase in equilibrium income 7. (b) the IS curve is vertical and the LM curve is upward sloping. 8. (b) 115.3 9. (d) 3/8

10. (d) A consumer’s budget share for an inferior good decreases with an increase in money income.

11. (b) Income elasticity of good x is 0. 12. (c) 1/3 13. (c) remains constant 14. (d) any of the above three conditions is satisfied 15. (c) f is quasi-convex 16. (a) does not change the value of the determinant of A 17. 1/25 18. (d) 0.82 19. (c) under flexible exchange rates when the exchange rate rises

(depreciates) above and then falls down to equilibrium after a monetary expansion

20. (c) fiscal policy is an effective tool for stabilizing the economy

Part - 2

21. (b) not a competitive equilibrium allocation but is pareto efficient 22. (a) a competitive equilibrium allocation and is pareto efficient


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23. (b) (0,1) 24. (c) 50 units 25. (a) equilibrium output increases by 160/3 units 26. (b) Current Employment: 400; Employment tomorrow: 424 27. (c) Rs. 4000 28. (b) 0.56 29. (b) q1=2 and q2=2 30. (b) A has x=2, y=0 and B has x=0, y=2 31. (a) 5/14 32. (d) 2/7 33. (b) 0 34. (b) 128 35. (b) has a greater impact on income than in a closed economy 36. (d) an increase in the interest sensitivity of money demand 37. (c) The line defined by y = x + 2 and the vertical axis. 38. (a) the smaller the induced change in interest rates and smaller the

responsiveness of investment to these changes 39. (d) the level of profits 40. (b) (x1, x2) = (2/18, 5/18) 41. (c) x1 increases and x2 decreases 42. (c) (15, 7) 43. (b) Y = 12500 – 50r 44. (d) does not change, ever increasing 45. (c) leaves unchanged 46. (d) 7/15 47. (b) 121/256 48. (c) 4/13 49. (a) 28/30 50. (d) Both countries produce both goods 51. (½)t2((1+b)/b) 52. (c) is greater than or equal to 0 at every x Є R 53. (d) In every election, every party has at least one dishonest candidate.


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54. (b) a Gang 55. (d) a Gang 56. (b) There are at least two sets of individuals that are both a Family and

a Gang. 57. (a) a Family 58. (a) 45 59. (b) 3/8 60. (d) f(x) = |x|, where x Є R and x ≥ 0


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DSE: Year 2007

Part - 1

1. (c) (20, 0) 2. (b) a vertical line 3. (b) K = (3/2)L 4. (c) MR < 0 in such a case 5. (a) A, B 6. (b) inflation is constant 7. (d) change the composition of monetary base 8. (a) always reduce borrowing 9. (a) improve it in the short run

10. (a) only raises the price level and the interest rate 11. (a) f(x) = x2 12. (c) det A = det B 13. (b) Df(x) = 0 for some x Є R 14. (d) In every legislature and every party, there exists a legislator who

does not pay taxes 15. (c) singular 16. (b) 2/5 17. (c) increases steadily from 0 to 1 18. (d) 4/7 19. (b) (i) 0.16; (ii) 0.29 20. (c) 7.5

Part - 2

21. (c) 1200-488L+72L2-4L3 22. (d) (i) Rs. 4,80,000 and (ii) risk-averse 23. (a) (i) 1 km and (ii) Rs. 100 24. (a) Some firms will exit the industry, but the others will remain


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25. (b) 9 apples 26. (a) 3.5 kg 27. (d) ((0, 0),(√8, 2),(3-√8, 1)) 28. (c) Pareto efficient, because there is a bound on Agent 1’s ability to

consume. 29. (b) √2 30. (c) ((0, 0), (0, 3-√3), (3, √3)) 31. λ/[α(1+λ)] 32. (b) P/Pe = 1+λ 33. (a) an increase in the actual price level 34. (b) a decrease in the actual price level 35. (a) β2/[1-(α1+β1)] units 36. (c) 1/[1-(α1+β1)+(Υ1β2)/Υ2] 37. (c) (1+δ)w2 > (1+r)w1 38. (a) goes up 39. (d) Country 1 has a lower equilibrium level of output than country 2

and it runs a trade surplus vis-à-vis Country 2. 40. (b) (i) and (ii) remain unchanged; (iii) depreciates 41. (a) {(x, r) | f(x) ≤ r} is convex 42. (a) 2xesqr(x)-ex 43. (d) converges to neither 1 nor -1 44. (d) [-1, 1] 45. (c) (-1, 1) 46. (d) d(x, z) ≤ d(x, y) +d(y, z) 47. (b) (A-B) X C = (A X C)-(B X C) 48. (c) Attains a saddle point 49. (c) 4.5 50. (d) During warm weather, my crops suffer from pests more than during

cooler weather. Therefore, a warm environment must help pests to multiply.

51. (d) None of the above 52. (3!3!)/6!


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53. (b) 5/18 54. (b) (½, ¾, ½) 55. (b) 37.6 years 56. (a) 0.025 57. (d) 5, 0.5, 39 58. (d) 0.79 59. (b) There is a significant difference in the performance of the classes at

the 5% level but no significant difference at the 1% level of significance 60. (b) There is no significant difference between the districts and the

candidate is preferred in district A


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DSE: Year 2008

Part - 1

1. (d) S1 and S3 (Fischer’s Index is ideal., it satisfies only these two) 2. (b) (0.1)(0.99)9 3. (d) The sample standard deviation is one third its original value 4. (c) III and IV 5. (c) g(y) = 2f(√y) for any y = 1, 4, …..,400 and g(y) = 0 otherwise. 6. (b) The goods are perfect substitutes 7. (c) price of good x is less than or equal to price of good y 8. (c) price must be higher in the market with lower price elasticity of

demand 9. (d) 5 and 10

10. (d) 1 11. (b) becomes flatter 12. (b) it leads to lower level of output in the equilibrium 13. (a) it leads to a higher steady state rate of growth 14. (c) expected currency depreciation must equal the currency differential

plus the risk premium. 15. (c) 1, 3 and 4 16. (d) g is a linear function, f is not linear 17. (b)-(yxy-1+zx In(z))/ (xzx-1+yz In(y)) 18. (c) a constant 19. (a) will change the sign of det A 20. (b) 3

Part - 2

21. (b) Rs. 3000 to 4000 22. (c) 0.95 and 0.55


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23. (a) A unit change in X is associated with a 1.25 unit change in Y, and a one unit change in Y is associated with a 0.6 unit change in X

24. (c) The probability that the life of the tyre will be between 336.84 and 363.16 days is 90%

25. (c) Given HA: π ‡ 0.1, we reject the null at the 10% level of significance, and the probability of error type I of this test is 0.1

26. (a) If HA: µ1-µ2 ‡ 0 we reject the null hypothesis at the 15%, 13%, 12% and 8% level of significance

27. (c) The chain base price indices with 2000 as base year are P01 = 148.3, P02 =154.2, and P03 =144.9

28. (d) 80/215 29. (b) only II and III 30. (c) 15/23 31. (a) (x2, y2) = (1-x1, 1-y1) for all x1, y1 Є [0, 1] 32. (d) Pareto Efficient 33. (b) (x1, y1) = (1, 1) and (x2, y2) = (1, 0) 34. (c) (px, py) = (1, 1) 35. (c) a subsidy of 1 to person 1 and a tax of 1 on person 2 36. (a) Ms A’s choices violate the weak axiom of revealed preference 37. (c) 5, 5, 2/5 38. (d) 5K2/(K2+F2) 39. (c) 10K2F2/(K2+F2) 40. (a) C*(x) = 2+2x, if x Є [0, 2]

4+x, if x > 2 41. (b) Ld = K(Aα)1/(1-α)(W/P)1/(α-1) 42. (a) shifts up 43. (a) Ls = L(W/P)β/(1-β)/(1+(W/P)β/(1-β)) 44. (b) shifts down 45. (d) W/P = [2+2√2]1/2 46. (c) vertical 47. (c) it increases by b/[b{1-c(1-τ)}+ad] units 48. (d) it decreases by b{1-c(1-τ)}/ [b{1-c(1-τ)}+ad] units


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49. (c) it increases by {M/(P)2}{1-c(1-τ)}/ [b{1-c(1-τ)}+ad] units 50. (b) downward sloping 51. (d) the rows of A are linearly independent 52. (a) strictly convex 53. (c) exactly one solution 54. (a) If Player 2 plays appropriately, he can win regardless of how 1

actually plays. 55. (d) limn→∞fn(x) exists for all but a finite set of real numbers 56. (c) a constant sequence 57. (b) a set having a single point 58. (a) eπ 59. (c) is discontinuous at x = 0 60. (c) are linearly dependent

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DSE -Entrance Solutions - Weeblysbcs.weebly.com/uploads/1/1/0/5/1105777/dsesolutions.pdf · DSE -Entrance Solutions Economics This document contains solutions of past year exam problems