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2010 

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. 

Amit Kumar Goyal 

economicsentrance.weebly.com, beaneconomist.com 

2/15/2010

Entrance Exam solutions economicsentrance.weebly.com beaneconomist.com 

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 

[2]


27. (d) 3/32 

28. (a) 2/3 

29. (c) 7.4 

30. 2p 2 

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)(p n-2 +(1-p) n-2 ) 

(b) (1- np(1-p)(p n-2 +(1-p) n-2 )) k-1 (np(1-p)(p n-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. 

[3]


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




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) 2p 2 

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 

[5]


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 

[6]




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 

[7]


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)t 2 ((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. 

[8]


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 

[9]




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) = x 2 

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+72L 2 -4L 3 

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 

[10]


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/P e = 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) 2xe sqr(x) -e x 

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! 

[11]


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 

[12]




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)-(yx y-1 +z x In(z))/ (xz x-1 +y z 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 

[13]


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) 5K 2 /(K 2 +F 2 ) 

39. (c) 10K 2 F 2 /(K 2 +F 2 ) 

40. (a) C*(x) = 2+2x, if x Є [0, 2] 

4+x, if x > 2 

41. (b) L d = K(Aα) 1/(1-α) (W/P) 1/(α-1) 

42. (a) shifts up 

43. (a) L s = 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 

[14]


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) e π 

59. (c) is discontinuous at x = 0 

60. (c) are linearly dependent 

[15]

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