IIT JAM 2021 question paper

All 60 questions from the IIT JAM 2021 IIT JAM Economics paper. Open any question for the worked solution.

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1. Q1When the expected future marginal product of capital increases, then the IS curve
2. Q2An unanticipated inflation would cause
3. Q3Let {x₁, x₂, ⋯, xₙ} be a sample with mean x̄, and let k be a real number other than x̄. Define S₁ = Σᵢ₌₁ⁿ (xᵢ - x̄)² and S₂ = Σᵢ₌₁ⁿ (xᵢ - k)². Then,
4. Q4You have a budget of Rs. 4000 and buy LPG cylinders at Rs. 50 each. If you return an empty cylinder purchased from the seller you get a refund of…
5. Q5Which one of the following is NOT a feature of the New Industrial Policy, 1991?
6. Q6Which one of the following is a possible reason for underestimation of the official poverty ratio in India?
7. Q7Which one of the following committees is NOT associated with financial sector reforms in India?
8. Q8The differential equation (3x² y + y³) dx + (x³ + 3xy²) dy = 0 is
9. Q9Which one of the following statements is correct?
10. Q10Let ‖·‖ and ⟨·,·⟩ denote the standard norm and inner product in ℝⁿ. If u, v ∈ ℝ³ with ‖u‖ = ‖v‖ = 2 and the angle between u and v is π/3, then
11. Q11A monopoly canteen serves two groups with demands Q_X = 200 - 4P and Q_Y = 300 - P, where P is the uniform price. The unit cost of each meal is Rs.…
12. Q12In a Solow model without technological progress, Yₜ = Kₜ^α Nₜ^(1-α), population grows at g_N > 0, saving rate s ∈ (0,1), depreciation δ ≥ 0, and kₜ…
13. Q13The utility from wealth is u(w) = √w. An individual owns a risky asset that is equally likely to yield Rs. 400 or Rs. 900. The risk premium of the…
14. Q14Let α̂₁ and α̂₂ be independent unbiased estimators of α with standard errors σ₁ and σ₂ (σ₁ ≠ σ₂). The linear combination of α̂₁ and α̂₂ that is…
15. Q15Let X be uniform on [0, b]. Testing H₀: b = 2 against H_A: b ≠ 2 uses the critical region {x ≤ 0.1 or x ≥ 1.9} from a single draw x. The probability…
16. Q16Let X be uniform on [a, b]. A sample of size five is {1.3, 0.8, 9.5, 20.2, 8.2}. The Maximum Likelihood Estimates â and b̂ are
17. Q17Two firms with identical technology have cost Cᵢ(qᵢ) = qᵢ². Market demand is p = 100 - q with q = q₁ + q₂. Assuming the firms are price takers, the…
18. Q18A paper mill has TB = 120Q - Q² and TC = 20Q, and its effluent creates an environmental cost EC = Q². The government imposes a production tax t per…
19. Q19Which one of the following statements is NOT correct regarding changes in the occupational structure of the workforce between 1951 and 1991 in India?
20. Q20Let W be the subspace of ℝ³ spanned by (0, -1, 2) and (2, -1, 0). Which one of the following vectors lies in W?
21. Q21Let f, g: ℝ → ℝ be f(x) = xe^(-x) and g(x) = x|x|. Then, on ℝ,
22. Q22(x₁* = 1, x₂* = 0, x₃* = 2) is optimal for: minimize x₁ + 5x₂ + 2x₃ subject to x₁ - x₂ ≤ 1, x₁ + x₂ + x₃ ≥ 3, x₁, x₂, x₃ ≥ 0. If (λ₁*, λ₂*) is an…
23. Q23X and Y are independent with F_X(x) = 1 - (3/4)^x and G_Y(y) = 1 - (2/3)^y for x, y = 1, 2, 3, …. Let Z = min {X, Y}. Then P(Z ≥ 6) is
24. Q24X and Y have joint density f_(X,Y)(x,y) = 6xy for 0 < y ≤ √x ≤ 1 and 0 otherwise. Then the conditional probability P(Y ≥ 1/3 | X = 2/3) is
25. Q25Which one of the following statements is NOT correct in the context of economic planning in India?
26. Q26For S₁, S₂ ⊂ ℝ define S₁ - S₂ = {x ∈ S₁, x ∉ S₂}. Let P = {x ∈ ℝ: x² - 2x - 3 ≤ 0} and Q = {x ∈ ℝ: log₅(1 + x²) ≤ 1}. Then,
27. Q27The workforce participation rate of a country is 60%. The country has a population of 100 million of which 6 million are unemployed. The…
28. Q28According to John Maynard Keynes, which one of the following statements is correct for a closed economy operating at less than the full employment…
29. Q29A monopolist faces a downward sloping linear market demand and his variable cost of production is zero. The profit maximizing price will
30. Q30X pays Rs. 5 lakhs to a person to transport fake currency worth Rs. 50 lakhs. The Police department pays Rs. 5 lakhs to a detective to investigate…
31. Q31An album has demand Q = 40000 - 800P and unit production cost Rs. 8. A profit-maximizing recording company offers the singer these contracts: (i)…
32. Q32Two firms with cost Cᵢ(qᵢ) = 10qᵢ compete in prices for a homogeneous good. Firm i faces demand 100 - pᵢ if pᵢ < pⱼ, 0 if pᵢ > pⱼ, and (100 - pᵢ)/2…
33. Q33Which of the following statements is/are correct about the Indian economy during the colonial period?
34. Q34In the context of the Expectations Augmented Phillips Curve (EAPC), which of the following statements is/are correct?
35. Q35Let f be defined on (-π/2, π/2) by f(x) = (cos (π/2 + |x|))/(sin (π/2 - |x|)). Then,
36. Q36Let x, y ∈ ℝ and M = [x+y x-y; x-y x+y]. If M[3; 1] = [-1; 3], then (with adj(M) the adjoint and det (M) the determinant)
37. Q37The net inflow of foreign currency on current and capital accounts combined is negative in a year. The country could be on a fixed or a flexible…
38. Q38Let k ∈ ℝ. Which of the following is/are correct for the roots of x² + 2(k+1)x + 9k - 5 = 0?
39. Q39If the number of employed workers in a country increases while its population does not change, then the unemployment rate in the country
40. Q40In a second-hand goods market, sellers H and L know their own product's quality but buyers cannot. Valuations rise with quality: H sells quality Q_H…
41. Q41Three independent rolls of a fair die determine winnings: Rs. 800 for three sixes, Rs. 400 for two sixes, Rs. 100 for exactly one six, and nothing…
42. Q42Full employment output is 1 trillion Rupees and the natural rate of unemployment is 6%. If actual unemployment is 8%, then by Okun's law the…
43. Q43Normalized dimension indices for a country are: standard of living 0.4, education 0.2, health 0.8. Following the current UNDP methodology, the Human…
44. Q44The value of the integral ∫₀⁹ (x - 1)/(1 + √x) dx is _ (in integer).
45. Q45Consider xₙ = ((n+1)/n)xₙ₋₁ for n = 1, 2, 3, … with x₀ = 2. Then x₁₀₀ - x₅₀ equals _ (in integer).
46. Q46In a small open economy, desired domestic savings S^d = 10 + 100 r^w and desired domestic investment I^d = 15 - 100 r^w, where r^w is the world real…
47. Q47Let X₁ ~ N(μ₁, σ₁²) and X₂ ~ N(μ₂, σ₂²) with μ₁ = 2, μ₂ = 3, σ₁² = 4, σ₂² = 9 and correlation coefficient 0.5. The variance of (X₁ + X₂) is _ (in…
48. Q48A consumer always spends 50% of monthly income on food. A value added tax raises food prices by 20% while income is unchanged. The consumer's price…
49. Q49A consumer's utility is u(x₁, x₂) = x₁ + 2√(x₂). At current prices and income the optimal bundle is (x₁ = 10, x₂ = 10). If income rises by 50% with…
50. Q50For a country's GDP in 2012-13 (local currency): GDP 59,816; private investment 17,811; exports 14,498; government investment 5,087; net factor…
51. Q51Amar has endowment F_A = 2, W_A = 5 and utility U_A = f_A² w_A. Barun has endowment F_B = 8, W_B = 5 and utility U_B = min {f_B, w_B}. They trade…
52. Q52A vaccine has supply q = 14 + 5p and demand q = 329 - 5p. The government sets a maximum price of Rs. 25 and subsidizes sellers per unit so the…
53. Q53A firm has two plants with TC₁ = 500 + 30Q₁ and TC₂ = 1500 + 20Q₂. Demand is Q^d = 150 - P/3. The value of Q₁ that maximizes the firm's profit is _…
54. Q54Let y(x) > 0 solve dy/dx + y = y². If y(ln 2) = 1/3, then y(ln 3) equals _ (round off to 2 decimal places).
55. Q55The optimal value of: minimize 2xy subject to 9x² + 4y² ≤ 36 is _ (in integer).
56. Q56For some β > 0, let x₁ and x₃ be the optimal basic feasible solution of: maximize x₁ + 2x₂ + 3x₃ subject to 2x₁ - x₂ + x₃ = 9, x₁ + 2x₂ - β x₃ = 1…
57. Q57Let X₁, X₂, X₃, X₄ be independent standard normal variables and Y = (X₁ + X₂)² + (X₃ + X₄)². The variance of Y equals _ (in integer).
58. Q58The aggregate production function is Y = 10N - 0.005N², where N is labour input, and labour supply is N = 55 + 5w with w the real wage. Assuming…
59. Q59Individuals earn and consume from age 18, retire at 60 and die at 90, leaving no debt or bequests. Income at age t is 100t - t². The price level is…
60. Q60An IS-LM closed economy has C = 200 + 0.8(Y - T) - 500r, I = 200 - 500r, T = 20 + 0.25Y, M^d/P = 0.5Y - 250(r + π^e). If G = 196, π^e = 0.1, nominal…