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Questions › DSE › DSE 2017

DSE 2017 question paper

All 50 questions from the DSE 2017 Delhi School of Economics MA entrance paper. Open any question for the worked solution.

  1. Q1Person A lexicographically prefers good x to good y: comparing two bundles she strictly prefers the one with more x, and if two bundles have equal x…
  2. Q2Person A has lexicographic preferences (strictly prefers more x; ties in x broken in favour of more y). Consider the bundle (2,1) and a sequence of…
  3. Q3An economy has two agents A and B and two goods x and y; both agents treat the goods as perfect complements. The total endowment is (4,2). Which of…
  4. Q4In an exchange economy with agents A and B and goods x and y, A 's endowment is (0,1) and B 's is (2,0) (only nonnegative consumption allowed). A…
  5. Q5In the exchange economy where A 's endowment is (0,1) and B 's is (2,0), with A lexicographically preferring x to y and B treating x and y as…
  6. Q6In the same exchange economy (A 's endowment (0,1), B 's endowment (2,0), B treating x and y as perfect substitutes), now suppose A…
  7. Q7In the same exchange economy (A 's endowment (0,1), B 's endowment (2,0)), suppose A lexicographically prefers y to x and B treats x and y as…
  8. Q8A sells an object by a sealed-bid auction with two bidders 1 and 2. Bidder i has valuation vᵢ and submits bid bᵢ; the object goes to the highest…
  9. Q9In the sealed-bid auction where the highest bidder wins and pays min {b₁,b₂}, with each valuation vᵢ private to bidder i, if bᵢ is the optimal bid…
  10. Q10The Nash equilibrium of the Cournot duopoly model is a pair of quantities (x₁,x₂) such that
  11. Q11Consider the Stackelberg duopoly model with firm 1 choosing quantity x₁ first; firm 2 observes x₁ and then sets x₂. The Nash (subgame-perfect)…
  12. Q12Consider the game (firm/player 1 chooses the row T or B, player 2 chooses the column L or R) with payoffs (a,b) = (row player, column player)…
  13. Q13A consumer has utility u(x,y,z)=y min {x,z}. All three goods have the same price and the consumer has Rs.\ 100 to spend on them. The demands will be…
  14. Q14A firm uses two inputs and, for all positive input prices, employs an input combination of the form (x,α x) where α>0 is a constant. Which…
  15. Q15Two telecom firms 1 and 2 have paid sunk spectrum fees k₁>0 and k₂>0 with k₁>k₂. They produce an identical service at the same constant average cost…
  16. Q16In a two-player game, player 1 first chooses U or D. Playing D ends the game with payoffs (1,0). Playing U lets player 2 choose U or D: player 2 's…
  17. Q17The interval (0,1) can be expressed as
  18. Q18The interval [0,1] can be expressed as
  19. Q19A function f:ℝⁿ→ℝ is a convex function if and only if
  20. Q20A function f:ℝⁿ→ℝ is a quasi-convex function if and only if
  21. Q21Let A={(x,y)∈ℝ²| x≥ 0, y≥ 0, xy≥ 1} and B={(x,y)∈ℝ²| x≤ 0, y≥ 0, xy≤ -1}, and let C={a+b| a∈ A, b∈ B}. Then
  22. Q22lim_(n→∞)(1+1/2n)⁵ⁿ equals
  23. Q23Consider f(x)=ln x for 0<x<1 and f(x)=ax²+b for 1≤ x<∞, with f(2)=3. Function f is continuous if
  24. Q24If A and B are n× n matrices such that A+B=AB, then
  25. Q25If B is an n× n real matrix and Bᵀ is its transpose, then
  26. Q26Let f:ℝ→ℝ be twice differentiable, with a<b, f(a)=0=f(b), and f′′(x)+f′(x)-1=0 for every x∈[a,b]. Then
  27. Q27Suppose f:ℝ₊→ℝ is decreasing and differentiable, and F:ℝ₊→ℝ satisfies F(x)=∫₀^x f(t) dt. Then F is
  28. Q28If real numbers p and q satisfy 0<q<p, then for the four numbers p, q, p+q, q-p:
  29. Q29If a binomial random variable X has expectation 7 and variance 2.1, then the probability that X=11 is
  30. Q30A machine starts at time 0 and fails at a random time T with density f(t)=1/3 e^(-t/3) for t>0. It is not monitored until t=2 (a failure before 2 is…
  31. Q31An insuree has a policy against a random loss X∈[0,1] with density f(x)=2x on (0,1); if loss X occurs the insurer pays X-C (the insuree bears…
  32. Q32A tour operator's bus seats 20; he sells 21 tickets because tourists may not show. Each tourist independently fails to show with probability 0.02.…
  33. Q33A policyholder submits up to 5 claims; pₙ is the probability of exactly n claims, n=0,…,5. It is known that (a) the difference pₙ-pₙ₊₁ is constant…
  34. Q34Suppose n students solve a problem starting at time 0; the completion time of student i is Tᵢ≥ 0, each uniformly distributed on [0,1]. If Y=max…
  35. Q35The weekly number of patients N satisfies P(N=n)=2⁻ⁿ⁻¹ for n≥ 0, independently across weeks. The probability that there are exactly seven patients…
  36. Q36X and Y have the joint distribution: for X=-1, P(Y=1)=0.1, P(Y=2)=α, P(Y=3)=0.3 (others 0); for X=1, P(Y=3)=β, P(Y=4)=P(Y=5)=P(Y=6)=0.1 (others 0).…
  37. Q37For the same joint distribution of X and Y (with X=-1 giving P(Y=1)=0.1, P(Y=2)=α, P(Y=3)=0.3 and X=1 giving P(Y=3)=β, P(Y=4)=P(Y=5)=P(Y=6)=0.1)…
  38. Q38An urn has 3 red and 5 black balls. Two balls are drawn in succession without replacing the first. The probability that the second ball is red equals
  39. Q39Let X and Y be independent standard Normal random variables, and let P(X>1)=p. The probability of the event {X²>1 and Y³<1} is
  40. Q40Suppose 1/10 of the population has a disease. If a person has the disease the test is positive with probability 8/10; if not, the test is (falsely)…
  41. Q41Two patients share a hospital room for two days. On any given day a person independently picks up an airborne infection with probability 1/4. Anyone…
  42. Q42Let w=W/P be the real wage. Labour demand is D(w)=1-w and labour supply is S(w)=w; with employment N, output is f(N). If the nominal wage always…
  43. Q43For the labour market with D(w)=1-w, S(w)=w (w=W/P), suppose the nominal wage W minimizes |D(W/P)-S(W/P)| subject to W≥ W₀, where W₀>0 is a minimum…
  44. Q44For the same labour market with wage floor (D(w)=1-w, S(w)=w, W=max {W₀,P/2}), given the price level P, the employment level is
  45. Q45For the labour market with wage floor, given a price level P such that 1/2≤ 1-W₀/P, the aggregate supply is
  46. Q46If the marginal productivity of capital is positive and the stock of capital increases, then the aggregate supply schedule will
  47. Q47If the fixed minimum nominal wage W₀ increases, then the aggregate supply schedule will
  48. Q48Consider a closed economy. If the nominal wage is flexible and the nominal money supply is increased, then in equilibrium which of the following is…
  49. Q49Which of the following would make the LM curve flatter in (Y,r) space?
  50. Q50In an IS-LM model with fixed exchange rates and perfect capital mobility, an increase in government spending will lead to