IIT JAM 2023 question paper

All 60 questions from the IIT JAM 2023 IIT JAM Economics paper. Open any question for the worked solution.

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1. Q1A competitive firm sells output at price P=1; production depends on capital alone, y=f(K), twice differentiable with f(0)=0, f′>0, f′′<0…
2. Q2Let f, g: ℝ → ℝ be f(x)=x+2 for x≤1, 2x+1 for x>1; and g(x)=2x for x≤2, x+2 for x>2. Then
3. Q3Let S be the feasible set of a linear programming problem (P). If the dual problem of (P) is unbounded, then
4. Q4Which of the following is NOT CORRECT?
5. Q5Which statement is CORRECT? S1: x²+y²=6 is a level curve of f(x,y)=√(x²+y²)-x²-y²+2. S2: x²-y²=-3 is a level curve of…
6. Q6Which of the following is NOT a component of Gross Domestic Product?
7. Q7Which of the following are instruments exercised by the Reserve Bank of India to control the money supply? (i) Cash Reserve Ratio (ii) Open Market…
8. Q8Which committee for the first time recommended for India (i) use of implicit prices from household consumer expenditure surveys for computing and…
9. Q9Which Five Year Plan focused on rapid industrialization (heavy and basic industries) and advocated a socialistic pattern of society as the goal of…
10. Q10Let M and N be events on a sample space S. If P(M)=1/3 and P(N^c)=1/4, which one is necessarily CORRECT?
11. Q11In a 2-agent, 2-good exchange economy, agent i has utility uᵢ(xᵢ,yᵢ)=max {xᵢ,yᵢ}. Endowments are (x̄₁,ȳ₁,x̄₂,ȳ₂)=(25,5,5,5). Which price vector…
12. Q12For a firm operating in a perfectly competitive market, which statement is CORRECT?
13. Q13A firm in a perfectly competitive environment sees a market change raise its profit by an amount K. Which describes the change in Producer's Surplus?
14. Q14Two people i∈{1,2} choose effort xᵢ∈[0,1] at cost Cᵢ(xᵢ)=xᵢ. The project's monetary outcome 4x₁x₂ is split equally. As a strategic game, the set of…
15. Q15Two firms X and Y operate in a perfectly competitive market. Their price elasticities of supply are 0.5 and 1.5 respectively. Then
16. Q16Let y=y(x) solve xdy/dx=yln (y/x), y>x>0. If y(1)=e² and y(2)=α, then dy/dx at (2,α) equals
17. Q17Let 2z=-3+√3 i, i=√(-1). Then 2z⁸ is equal to
18. Q18Let aₙ=(1+1/n)^(n/2) be the n th term of ⟨ aₙ⟩. Which one is NOT CORRECT?
19. Q19For the LP (P): minimise z=4x₁+6x₂+6x₃ subject to x₁+3x₂≥3, x₁+2x₃≥5, x≥0. If x* is optimal, z* the optimal value, and w*=(w₁*,w₂*) the dual…
20. Q20For α,β∈ℝ, consider x+y+z=1, 3x+y+2z=2, 5x+α y+β z=3. Then
21. Q21For a positively sloped LM curve, which statement is CORRECT?
22. Q22An economy produces only apples and bananas. 2010: apple price 1 (qty 100), banana price 2 (qty 50); 2011: apple 1 (200), banana 2 (100); 2012…
23. Q23Which statement is NOT CORRECT for an open-economy IS-LM model under a floating exchange rate (fixed price) and perfect capital mobility?
24. Q24Which statement is CORRECT? S1: Structural unemployment arises between two jobs, the first quit to find the second. S2: Frictional unemployment…
25. Q25Match List-I with List-II. (a) Fiscal Deficit (b) Revenue Deficit (c) Primary Deficit; (i) revenue expenditure minus revenue receipts (ii) total…
26. Q26A production function Yₜ=AₜKₜ^αLₜ^(1-α), α∈(0,1). With per-capita output y=Y/L and capital-output ratio k=K/Y, and ẋ denoting dx/dt, the per-capita…
27. Q27Match the regulator to the year it became a statutory body via a Parliamentary Act. (a) RBI (b) SEBI (c) IRDAI (d) IBBI; (i) 2016 (ii) 1934 (iii)…
28. Q28Let X~Normal(0,1) and Y=|X|. If the pdf of Y is f_Y(y), then for y>0, √(π/2) f_Y(y) is
29. Q29Let X have pdf f_X(x,λ)=λ e^(-λ x) for x≥0 (λ>0). For the sample 1.75, 2.25, 2.50, 2.75, 3.25, the Maximum Likelihood Estimator of λ is
30. Q30From 10 students (four girls Gᵢ, six boys Bⱼ), a team of five is formed. The probability that a randomly selected team has 2 girls and 3 boys, with…
31. Q31Suppose u:ℝⁿ₊→ℝ₊ represents a complete, transitive, continuous preference relation. Which functions also represent the same preference relation?
32. Q32A 2-agent, 2-good economy has aggregate endowment 30 of X and 10 of Y, with uᵢ(xᵢ,yᵢ)=max {xᵢ,yᵢ}. Which allocations (x₁,y₁,x₂,y₂) are Pareto optimal?
33. Q33In a 3-player game (Player 1: Up/Down, Player 2: Left/Right, Player 3: Table 1/Table 2), payoffs are Table 1 [Up: (3,2,5),(4,1,3); Down…
34. Q34Let f(x,y)=(x²-y³)/(x²+y²) for (x,y)≠(0,0) and f(0,0)=0. Then
35. Q35For α,β∈ℝ, α≠β, if -2 and 5 are eigenvalues of M=[1-α 1+β; β α+β] and X=[x₁,x₂]ᵀ is an eigenvector for -2, then
36. Q36Which statements are CORRECT for the Absolute Income Hypothesis?
37. Q37With GDP_F = GDP at factor cost, GDP_M = GDP at market price, NNP_F = Net National Product at factor cost, and standard symbols C,I,G,X,M,T,S,D,NIA…
38. Q38Which major developments were undertaken after the 1991 structural reforms of the Indian economy?
39. Q39Which functions qualify as a cumulative distribution function of a random variable X? (A) 1-e^(-x) on (0,∞), else 0. (B) (1+e^(-x))⁻¹ on ℝ. (C)…
40. Q40Let f(x,y)=1 for 0<x<1, x<y<x+1, and 0 otherwise. Which are CORRECT for the marginals and moments?
41. Q41Let X~Uniform(8,20) and Z~Uniform(0,6) be independent. Let Y=X+Z and W=X-Z. Then Cov(Y,W) is (in integer).
42. Q42Let Y~Normal(3,1), W~Normal(1,2) and X~Bernoulli(p=0.9) (X=1 success). Let S=XY+(1-X)W. Then E(S)= (round off to 1 decimal place).
43. Q43If X is the sum on a throw of two fair six-faced dice, then P(7<X<10)= (round off to 2 decimal places).
44. Q44Given 2010: population 20,000, GDP 25,000 crore; 2020: population 25,000, GDP 40,000 crore. The average (compound annual) growth rate of per-capita…
45. Q45In a Keynesian Cross model with C=C₀+b(Y-T), T=T₀+tY, Y=C+I₀+G₀, and b=0.7, t=0.2, the value of the Keynesian multiplier is (round off to 2 decimal…
46. Q46Let [t] denote the greatest integer ≤ t. The number of points of discontinuity of f(x)=[ x²-3x+2 ] for x∈[0,4] is (in integer).
47. Q47Let E be the area of the region bounded by y=x² and y=8√x, x≥0. Then 30E is equal to (round off to 1 decimal place).
48. Q48A firm has production function y=K⁰·⁵L⁰·⁵ and faces w=4, r=4. The firm's marginal cost is equal to (in integer).
49. Q49Let ŷ=5.5+3.2x be estimated on a large sample. The 95% confidence interval of the coefficient of x is [0.26, 6.14] and R²=0.26. The standard error…
50. Q50Let π be the proportion vaccinated, with estimate π̂=0.64 from n=100. The z test statistic for H₀:π=0.58 is (round off to 2 decimal places).
51. Q51An industry has 3 Cournot firms with zero fixed cost and marginal costs c₁=9/30, c₂=10/30, c₃=11/30, facing P=1-Q. If Q^c is the Cournot-Nash…
52. Q52A consumer has u(x₁,x₂)=max {0.5x₁,0.5x₂}+min {x₁,x₂} with income y, p₂=1. There is a lowest price p̄₁ such that if p₁>p̄₁ the unique optimum is to…
53. Q53Firm X 's output creates a benefit of INR 700 for Y and a cost of INR 300 for Z per unit. X 's cost is C(Q_X)=2Q_X²+10, and the market price is INR…
54. Q54Let ∫ sin⁹ xcos (11x) dx=cos (10x)f(x)+c. If f′′(π/4)-k f′(π/4)=0, then k is equal to (in integer).
55. Q55Let M=[k 1 1; 1 k 1; 1 1 k] and I₃ the identity. If the rank of 10I₃-M is 2, then k is equal to (in integer).
56. Q56In a two-period model, a consumer maximises Wₜ=ln (cₜ)+1/(1+θ)ln (cₜ₊₁) subject to cₜ+cₜ₊₁/(1+r)≤ yₜ+yₜ₊₁/(1+r). With θ=0.05, r=0.08, the interior…
57. Q57A portfolio has R=wRₛ+(1-w)R_T with Var(Rₛ)=0.07, Var(R_T)=0.05, Cov(Rₛ,R_T)=0.04. The w minimising Var(R) is (round off to 2 decimal places).
58. Q58A number x is randomly chosen from the first 100 natural numbers. The probability that x satisfies x+300/x>65 is (round off to 2 decimal places).
59. Q59For k∈ℝ, let f(x)=x⁴+2x³+kx²-k. If x=3/2 is a local minimum of f and m is the global minimum value, then f(0)-m is (in integer).
60. Q60If (x*,y*) solves: maximise f(x,y)=100-e^(-x)-e^(-y) subject to ex+y=e/(e-1), x≥0, y≥0, then √(y*/x*) is (round off to 2 decimal places).