DSE 2010 question paper

All 60 questions from the DSE 2010 Delhi School of Economics MA entrance paper. Open any question for the worked solution.

1. Q1In models where expectations adjust slowly, a progressive income tax schedule is
2. Q2Open market operations decrease the supply of base money by
3. Q3If an economy is experiencing hyperinflation, then
4. Q4When the nominal interest rate changes but the real rate of interest remains unchanged
5. Q5Ceteris paribus, higher velocity of money circulation leads to
6. Q6Consider a 3× 3 nonsingular matrix A with real entries. If the matrix B is derived from A by interchanging the first and last columns of A, then the…
7. Q7The sequence (-1)ⁿ(1+1/n), for positive integers n,
8. Q8Consider two games. Game 1: the row player chooses Enter or Not enter and the column player's only option is Hawk, payoffs (row, column) Enter…
9. Q9Ice-cream vendors A and B locate simultaneously on a beach identified with the interval [0,1]; at every point there is a buyer who buys from the…
10. Q10There is one future period with two possible states s₁,s₂. A share returns 5 in s₁ and -1 in s₂, priced at 3. A government bond returns 1 in each…
11. Q11A number X₁ is chosen at random from the set {1,2}. Then a number X₂ is chosen at random from the set {1,X₁}. The probability that X₁=2 given that…
12. Q12Suppose a random variable X takes values -2,0,1 and 4 with probabilities 0.4,0.1,0.3 and 0.2 respectively.
13. Q13Two persons A and B shoot at a target. A hits on any shot with probability 1/3 and B with probability 1/4. A shoots first and they take turns. What…
14. Q14A fair coin is tossed repeatedly until a head is obtained for the first time. Let X denote the number of tosses required. The value of the…
15. Q15Using a random sample, an OLS regression of Y on X yields the 95% confidence interval 0.43<β<0.59 for the slope parameter β. Which of the following…
16. Q16Consider a binary relation ⪰ on A={x,y,z}. Define ≻ and ~ by: a≻ b iff a⪰ b and not b⪰ a; a~ b iff a⪰ b and b⪰ a. Suppose x≻ y, y~ z and x~ z. Then
17. Q17The utility function u(x,y)=(x+y)^(1/2), for (x,y)≥ (0,0), exhibits
18. Q18Suppose there are just two goods, x₁ and x₂. A consumer chooses x₂=0 for all income levels w>0 and all prices p₁>0,p₂>0. These choices are…
19. Q19Consider a Cournot duopoly with firms 1 and 2 producing a homogeneous good, inverse demand P(x)=5-x where x is total output. Firm 1 has constant…
20. Q20If all input prices double, then what happens to the minimum cost of producing a given output?
21. Q21Consider a closed economy. If the nominal wage is flexible and nominal money supply is increased, then which of the following will be true in…
22. Q22An economy is at less than full employment with an aggregate 'worker' and an aggregate 'capitalist', the worker having a higher marginal propensity…
23. Q23Consider an economy with aggregate production Y=α K+β L, α,β>0, K fixed in the short run. Competitive producers take the nominal wage W and price P…
24. Q24Assume the parametric condition of the previous question holds and the nominal wage is fixed. The short run aggregate supply schedule, with P on the…
25. Q25If there is a one shot increase in the fixed stock of capital, then the short run aggregate supply schedule will
26. Q26If there is a one shot increase in the fixed nominal wage rate, then the short run aggregate supply schedule will
27. Q27Consider a closed-economy Keynesian model: prices fixed, output determined by aggregate demand, investment fixed at I*, no government. Two household…
28. Q28(Same two-group model.) If there is a one shot increase in the parameter λ,
29. Q29(Same two-group model.) If there is a one shot increase in the parameter c_A,
30. Q30(Same two-group model.) If there is a one shot increase in the parameter c_B,
31. Q31Suppose the function f:ℜ→ℜ is given by f(x)=x³-3x+b. Find the number of points in the closed interval [-1,1] at which f(x)=0.
32. Q32Suppose a function f:ℜ→ℜ is differentiable at x. Consider the statements: (i) Df(x)=lim_(h→ 0)(f(x)-f(x-h))/h; (ii) Df(x)=lim_(h→…
33. Q33Consider the statements for x,y∈ℜ: (i) |x|-|y|≤ |x-y|; (ii) | x|-|y | =|x-y|. In general,
34. Q34Suppose f:ℜ²→ℜ is increasing in both arguments. For x,y∈ℜ let x∧ y=x if x≤ y and =y if x>y. Define g:ℜ²→ℜ by g(x,y)=f(x,y)-1/2f(x∧ y,x∧ y) if x≥ y…
35. Q35Let A={(x,y)∈ℜ²| x²+y²≤ 1}. Given (a,b)≠(0,0) and c>1, let X={(x,y)+(a,b)| (x,y)∈ A}, Y={(2^(-1/2)(x+y),2^(-1/2)(x-y))| (x,y)∈ A}, Z={c(x,y)| (x,y)∈…
36. Q36(Same definitions of A,X,Y,Z .) Which set has a larger area than A?
37. Q37(Same definitions of A,X,Y,Z .) Which set does not contain all the points that belong to A?
38. Q38Consider a twice differentiable function f:ℜ→ℜ and a,b∈ℜ with a<b, f(a)=0=f(b) and D²f(x)+Df(x)-1=0 for every x∈[a,b]. Then,
39. Q39Consider f as described in the previous question. Then,
40. Q40Suppose f:[0,1]→[0,1] is a continuous nondecreasing function with f(0)=0 and f(1)=1. Define g:[0,1]→[0,1] by g(y)=min {x∈[0,1]| f(x)≥ y}. Then,
41. Q41Suppose X₁ and X₂ are real-valued random variables with f as their common probability density function, and (x₁,x₂) is a sample generated by them.…
42. Q42Suppose X₁,…,Xₙ are observed completion times uniformly distributed on [0,1]. If Y is the maximum observed completion time, then the mean of Y is
43. Q43Suppose the random variable X takes values in {-1,0,1} with equal probability. Let Y=X². Which of the following statements is true?
44. Q44Suppose player 1 has five coins and player 2 has four coins. Both players toss all their coins and observe the number that come up heads. Assuming…
45. Q45Suppose 10 athletes are running in a race and exactly 2 of them are taking banned drugs. An investigator randomly selects 2 athletes for…
46. Q46Suppose θ is a random variable with uniform distribution on [-π/2,π/2]. The value of the distribution function of the random variable X=sin θ at…
47. Q47Let X be a normally distributed random variable with mean 0 and variance σ². Then, the mean of X² is
48. Q48The number of loaves of bread sold by a bakery in a day is a random variable X with density f(x)=kx for x∈[0,5), f(x)=k(10-x) for x∈[5,10), and 0…
49. Q49(Same bakery density.) Let A be the event X≥ 5 and B the event X∈[3,8]. The probability of A conditional on B is
50. Q50(Same bakery density.) Events A (X≥ 5) and B (X∈[3,8]) are
51. Q51Consider an exchange economy with agents 1 and 2 and goods x,y. Agent 1's endowment is (0,1) and agent 2's is (2,0); only nonnegative consumption is…
52. Q52(Same economy, agent 1 lexicographic for x, agent 2 perfect substitutes.) The set of all possible competitive equilibrium prices consists of all…
53. Q53Now suppose agent 1 lexicographically prefers y to x and agent 2 treats x and y as perfect substitutes. The set of all possible competitive…
54. Q54Now suppose agent 1 lexicographically prefers y to x and agent 2 treats x and y as perfect complements. The set of competitive equilibrium allocations
55. Q55A person chooses among lotteries (p₁,p₂,p₃) where p₁,p₂,p₃ are the probabilities of getting Rs. 5, Rs. 1 and Rs. 0. This person prefers lottery…
56. Q56Consider an economy with two agents A and B and two goods x₁,x₂. Both agents treat x₁ and x₂ as perfect complements. The total endowment of x₁ is 4…
57. Q57A consumer has utility u(x,y)=xy and demands bundle (x*,y*). Now the seller of good x offers a 'buy one, get one free' scheme: for each unit of x…
58. Q58Consider a Bertrand duopoly with firms 1 and 2 producing a homogeneous good and setting prices p₁,p₂ that must be positive integers. If p₁<p₂ (resp.…
59. Q59Consider a Stackelberg duopoly with firm 1 as leader and firm 2 as follower. If (q₁,q₂) is the Stackelberg equilibrium, then
60. Q60Firm 1 is a potential entrant into a market where firm 2 is the incumbent. Firm 1 moves first, choosing 'enter' or 'not enter'. If it does not…