DSE 2008 question paper

All 60 questions from the DSE 2008 Delhi School of Economics MA entrance paper. Open any question for the worked solution.

1. Q1In the context of ideal price index numbers, consider: S1: the index should be invariant to the choice of base, i.e. Pᵣₛ· Pₛᵣ=1. S2: an index that…
2. Q2Suppose the probability that any particle emitted by a radioactive material will penetrate a given shield is .01. If ten particles are emitted, what…
3. Q3Consider a symmetric 90% confidence interval for the population mean of a normal distribution with unknown variance, constructed using a random…
4. Q4Let A and B be any two events, each with a positive probability of occurring. Consider: I. If A and B are independent, they must be mutually…
5. Q5A random variable X takes only nonzero integer values from -20 to +20, with a probability mass function f(x) symmetric around 0. Consider Y=X².…
6. Q6A consumer has a utility function U(x,y)=10(x²+4xy+4y²)+20. Which one of the following statements must be true?
7. Q7Suppose a consumer has utility function U=min {x+y, 2y}. He maximizes utility subject to his budget constraint and consumes (x*,y*)=(3,3). Which one…
8. Q8Suppose a monopolist sells his product in two separate markets. After the product is sold in one market, there is no possibility of it being resold…
9. Q9Consider a firm producing a single good with the cost function C(x)=5 if x=0, and C(x)=10+10x if x>0. This firm's sunk cost and fixed cost are…
10. Q10The elasticity of substitution of the production function f(x,y)=cx^ay^b is
11. Q11In the standard IS-LM framework, if you introduce endogenous money supply such that money supply depends positively on the nominal rate of interest…
12. Q12Consider a simple Keynesian model where equilibrium output is determined by aggregate demand. Investment is autonomous and a constant proportion of…
13. Q13In the Solow model of growth, an increase in the savings propensity has the following impact:
14. Q14If covered interest parity prevails between two countries,
15. Q15Which of the following constitute the 'impossible trinity' which cannot be simultaneously ensured in an open economy? 1. Fixed exchange rate; 2.…
16. Q16Consider two functions mapping points on the plane back to points on the plane: (i) f(x₁,x₂)=(x₁+1, x₂+1) and (ii) g(x₁,x₂)=(x₂,x₁). Which of the…
17. Q17Consider the equation x^y+y^z+z^x=k, defined for all positive values of x,y,z, where k is a given positive constant. The partial derivative ∂ z/∂ x…
18. Q18The derivative of the function defined by f(x)=sin²x+cos²x is
19. Q19Consider an n× n real matrix A with n>4. Interchanging the positions of two columns
20. Q20Suppose we have a chair with n legs and it stands with all its legs touching the floor, regardless of the floor quality, i.e., evenness, smoothness…
21. Q21The frequency distribution of variable X (monthly family expenditure in Rs. '000) for 100 households is: class 10 - 15 has 10 households, 5 - 9.9999…
22. Q22The frequency distribution of variable Y, the number of heads when two damaged coins are tossed, is: F(0)=0.3, F(1)=0.45, F(2)=0.25 (these are the…
23. Q23For variables X and Y we have the data Σ XY=350, Σ X=50, Σ Y=60, X̅=5, σ_X²=4, σ_Y²=9. Which of the following holds?
24. Q24The life of a cycle tyre is normally distributed with mean 350 days and variance 64. It is true that:
25. Q25In a random sample of 400 mangoes from a large consignment, 30 were found rotten. The null hypothesis is that the proportion π of rotten mangoes is…
26. Q26In a sample of 1000 mangoes, the mean weight is 210 g with standard deviation 9.5 g. In another sample of 1200 mangoes, the mean is 180 g with…
27. Q27Data on India's exports of Jute and Tea, 2000-2003: Jute quantity ('000 t) 871, 706, 724, 627 and price (Rs '00000/1000 t) 202, 320, 311, 302; Tea…
28. Q28Suppose that 80% of all statisticians are shy, whereas only 15% of all economists are shy. Suppose also that 90% of the people at a large gathering…
29. Q29Each cell of the following table gives the joint probability of (X,Y). For X=1: Y=1→.1, Y=2→0, Y=3→.1, Y=4→0. For X=2: .3, 0,.1,.2. For X=3: 0,.1…
30. Q30A survey of poor rural households finds 40% own a radio, 15% own a television and 60% own a bicycle. Also 5% own both radio and television, 26% own…
31. Q31Consider an exchange economy with two persons and two goods. Person 1's utility is u₁(x,y)=x+y and person 2's is u₂(x,y)=e^(x²+y²+2xy). Person 1's…
32. Q32Consider an exchange economy with persons 1 and 2 and goods x and y. Person 1's utility is u₁(x,y)=x²y² and person 2's is u₂(x,y)=e^(x+y). The total…
33. Q33Consider the situation of the preceding question (u₁=x²y², u₂=e^(x+y), total endowment (2,1)). If person 1's endowment is (1,1) and person 2's is…
34. Q34Consider the situation of the preceding question. Which of the following is an equilibrium price vector?
35. Q35Consider an exchange economy with the same two agents and utility functions as the last three questions, but now the endowments are (0,1) and (2,0).…
36. Q36There are 3 items of choice, x,y,z, and Ms. A has 4 choice situations: in 3 of them she is asked to choose one or more items from the pairs {x,y}…
37. Q37A chemical factory produces chemical K and an effluent E dumped in a river; a downstream fishery produces fish F, its costs affected by E. Both…
38. Q38Suppose the socially optimal levels K̅,E̅,F̅ maximize the joint profit of an integrated firm combining the factory and the fishery. Then E̅ equals
39. Q39Suppose a government knows the firms' production functions and output prices, and can costlessly monitor the effluent released by the chemical…
40. Q40Consider a firm with one output and two possible choices of capital stock, 1 and 2. The associated cost functions are C(x,1)=2+2x and C(x,2)=4+x.…
41. Q41Consider a macro-economy with short-run aggregate output Y=AL^α(K̅)^(1-α), where L is labour, K̅ the fixed capital stock, A>0, 0<α<1. P is the price…
42. Q42If there is a one-shot increase in the stock of capital (K̅), the demand for labour schedule, as derived above,
43. Q43Suppose the economy has a single household with total labour endowment L̅, supplying L^s to the market at money wage W and enjoying the rest as…
44. Q44If there is an exogenous increase in the total endowment of labour time (L̅), the supply of labour schedule, as derived above,
45. Q45Let α=1/2, β=2/3, K̅=10, L̅=10, A=4. Given these parameter values, the unique non-negative equilibrium value of the real wage rate that clears the…
46. Q46Given the labour demand and labour supply schedules derived above, the aggregate supply curve (output supplied as a function of the aggregate price…
47. Q47Consider a closed economy with P̅ fixed: Y=C+I+G, C=c(Y-T) with 0<c<1, I=I̅-dr (d>0), T=τ Y (0<τ<1), G=G̅, money market M̅/P̅=L=aY-bi (a,b>0), and…
48. Q48(Same model.) In ceteris paribus, a unit increase in the expected rate of inflation has the following impact on the equilibrium value of the real…
49. Q49(Same model.) In ceteris paribus, a unit increase in the general price level has the following impact on the equilibrium value of the real interest…
50. Q50(Same model.) Suppose we now allow the general price level to be flexible. Given the above characteristics, the aggregate demand curve (output…
51. Q51Fix an m× n matrix A and an m -vector b. A condition that ensures the existence of a solution (an n -vector x) of the equation Ax=b is
52. Q52The real-valued function f(x)=x³ is
53. Q53Consider the equation Ax=0 where A is an n× n matrix such that aᵢᵢ≠ 0 for every i∈{1,…,n} and aᵢⱼ=0 whenever i>j. This equation has
54. Q54There is a pile of 17 matchsticks. Players 1 and 2 take turns removing sticks, starting with Player 1. On each turn a player removes a number of…
55. Q55If A is a set of real numbers, let g_A(x)=1 if x∈ A and 0 if x∉ A. Consider the sequence of functions fₙ(x)=n g_([0,1/n])(x) for all real x and each…
56. Q56Continuing with the sequence of functions above, consider the sequence of real numbers (∫ fₙ)ₙ₌₁^∞ (the sequence of their integrals). This sequence…
57. Q57For each positive integer a=1,2,3,…, let Sₐ be the set of points on the curve y=1/x^a for all positive real x. Then the intersection ⋂ₐ₌₁^∞Sₐ is
58. Q58Which of the following two numbers is larger: e^π or π^e?
59. Q59The function f(x)=sin (1/x) if x>0 and f(x)=a if x=0 (with f defined for x≥ 0)
60. Q60Suppose v₁,v₂ and v₃ are three vectors in 3-dimensional space and are linearly dependent. Then the vectors v₁+v₂, v₂+v₃, and v₁+v₃