JAM 2021 Economics (EN) PDF

JAM 2021 Economics (EN) SECTION – A MULTIPLE CHOICE QUESTIONS (MCQ) Q.1 – Q.10 Carry ONE mark each. Q.1 When the expected future marginal product of capital increases,...

JAM 2021 Economics (EN) SECTION – A MULTIPLE CHOICE QUESTIONS (MCQ) Q.1 – Q.10 Carry ONE mark each. Q.1 When the expected future marginal product of capital increases, then the IS curve (A) shifts up and to the right (B) shifts down and to the left (C) becomes steeper (D) becomes flatter Q.2 An unanticipated inflation would cause (A) redistribution of wealth from lenders to borrowers (B) redistribution of wealth from borrowers to lenders (C) gains for both borrowers and lenders (D) losses for both borrowers and lenders EN Page 1 of 34 JAM 2021 Economics (EN) Q.3 Let {𝑥1 , 𝑥2 , ⋯ , 𝑥𝑛 } be the realization of a randomly drawn sample of size 𝑛 with sample mean 𝑥̅ , and 𝑘 be a real number other than 𝑥̅. Let 𝑆1 and 𝑆2 be the sums of squared deviations defined as 𝑛 𝑛 𝑆1 = ∑(𝑥𝑖 − 𝑥̅ )2 and 𝑆2 = ∑(𝑥𝑖 − 𝑘 )2. 𝑖=1 𝑖=1 Then, (A) 𝑆1 > 𝑆2 (B) 𝑆1 > 𝑆2 only if 𝑥̅ < 𝑘 (C) 𝑆1 < 𝑆2 (D) 𝑆1 > 𝑆2 only if 𝑥̅ > 𝑘 Q.4 You have a budget of Rs. 4000 and would like to purchase LPG cylinders from a local seller who charges Rs. 50 per cylinder. The seller has a subsidy scheme by which if you return the empty cylinder purchased from him, you will get a refund of Rs. 20 per cylinder. You cannot borrow money from anyone. The maximum number of cylinders you can purchase is (A) 131 (B) 132 (C) 133 (D) 134 EN Page 2 of 34 JAM 2021 Economics (EN) Q.5 Which one of the following is NOT a feature of the New Industrial Policy, 1991? (A) Abolition of industrial licensing (B) Privatisation of public industries (C) Removal of restrictions on foreign trade (D) Restrictions on foreign technology agreements Q.6 Which one of the following is a possible reason for underestimation of the official poverty ratio in India? (A) Changes in the World Bank’s definition of poverty (B) Price indices used in the official poverty estimation may not be adequately capturing the actual increase in the cost of living over the years (C) Existence of identical poverty lines for all the states and union territories (D) Existence of identical poverty lines for rural and urban areas EN Page 3 of 34 JAM 2021 Economics (EN) Q.7 Which one of the following committees is NOT associated with financial sector reforms in India? (A) Raghuram Rajan Committee (2013) (B) Narasimham Committee (1991) (C) Tarapore Committee (1997) (D) Urjit Patel Committee (2013) Q.8 The differential equation (3𝑥 2 𝑦 + 𝑦 3 )𝑑𝑥 + (𝑥 3 + 3𝑥𝑦 2 )𝑑𝑦 = 0 is (A) homogenous and exact (B) neither separable nor exact (C) exact and not homogenous (D) homogenous and not exact EN Page 4 of 34 JAM 2021 Economics (EN) Q.9 Which one of the following statements is correct? (A) If 〈 𝑎𝑛 〉 is a bounded sequence, then it is convergent (B) If 〈 𝑎𝑛 〉 is a convergent sequence, then it is monotonic (C) If 〈 𝑎𝑛 〉 is a convergent sequence and converges to zero, then the series ∑∞ 𝑛=1 𝑎𝑛 is convergent (D) If a series ∑∞ 𝑛=1 𝑎𝑛 is convergent, then the sequence 〈 𝑎𝑛 〉 is convergent and converges to zero Q.10 Let ||. || and 〈. ,. 〉 denote the standard norm and inner product in ℝ𝑛 , respectively. If 𝑢 , 𝑣 ∈ ℝ3 such that || 𝑢 || = || 𝑣 || = 2 and the angle between 𝑢 and 𝑣 is 𝜋⁄3 then (A) || 𝑢 − 𝑣 || = 2√2 (B) 〈 𝑢 , 𝑣 〉 = 2√3 (C) || 𝑢 − 𝑣 || = 2√3 (D) || 𝑢 + 𝑣 || = 2√3 EN Page 5 of 34 JAM 2021 Economics (EN) Q. 11 – Q. 30 Carry TWO marks each. Q.11 A monopoly canteen serves packed meals to two groups of consumers, group 𝑋 and group 𝑌. The demand for packed meals for 𝑋 and 𝑌 are given by, 𝑄𝑋 = 200 − 4𝑃 and 𝑄𝑌 = 300 − 𝑃, where 𝑃 is the uniform price per unit. The unit cost of producing each meal is Rs. 50. The value of 𝑃 (in Rs.) that maximizes the canteen’s profit is (A) 75 (B) 50 (C) 125 (D) 175 EN Page 6 of 34 JAM 2021 Economics (EN) Q.12 Consider a Solow growth model without technological progress. The production function is 𝑌𝑡 = 𝐾𝑡𝛼 𝑁𝑡1−𝛼 where 𝑌𝑡 , 𝐾𝑡 and 𝑁𝑡 are the aggregate output, capital and population at time 𝑡, respectively. The population grows at a constant rate of 𝑔𝑁 > 0, savings rate is constant at 𝑠 ∈ (0,1) and capital depreciates at a constant rate of 𝛿 ≥ 0. Denote per capita capital as 𝑘𝑡 = 𝐾𝑡 /𝑁𝑡 and define the steady state as a situation where 𝑘𝑡+1 = 𝑘𝑡 = 𝑘 ∗ where 𝑘 ∗ is a positive constant. Suppose the population growth rate exogenously increases to 𝑔𝑁′. At the new steady state, the aggregate output will grow at a rate (A) 𝑔𝑁 (B) 𝑔𝑁′ (C) (1 − 𝛼)𝑔𝑁 (D) (1 − 𝛼)𝑔𝑁′ EN Page 7 of 34 JAM 2021 Economics (EN) Q.13 The utility from wealth (𝑤) for an individual is given by 𝑢(𝑤) = √𝑤. The individual owns a risky asset that is equally likely to yield either Rs. 400 or Rs. 900. The risk premium of the asset (in Rs.) is (A) 5 (B) 25 (C) 625 (D) 650 Q.14 Let 𝛼 ̂1 and 𝛼 ̂2 be two independent unbiased estimators of the parameter 𝛼 with standard errors 𝜎1 and 𝜎2 , respectively, with 𝜎1 ≠ 𝜎2. The linear combination of 𝛼 ̂1 and 𝛼 ̂2 that yields an unbiased estimator of 𝛼 with the minimum variance is (A) ( 𝜎1 𝜎2 )𝛼 ̂1 + ( )𝛼 ̂ 𝜎1 + 𝜎2 𝜎1 + 𝜎2 2 (B) ( 𝜎2 𝜎1 )𝛼 ̂1 + ( )𝛼 ̂ 𝜎1 + 𝜎2 𝜎1 + 𝜎2 2 (C) 𝜎12 𝜎22 ( 2 )𝛼 ̂+( 2 )𝛼 ̂ 𝜎1 + 𝜎22 1 𝜎1 + 𝜎22 2 (D) 𝜎22 𝜎12 ( 2 )𝛼 ̂+( 2 )𝛼 ̂ 𝜎1 + 𝜎22 1 𝜎1 + 𝜎22 2 EN Page 8 of 34 JAM 2021 Economics (EN) Q.15 Let 𝑋 be a uniformly distributed random variable in [0, 𝑏]. If the critical region for testing the null hypothesis 𝐻0 : 𝑏 = 2 against the alternative hypothesis 𝐻𝐴 : 𝑏 ≠ 2 is {𝑥 ≤ 0.1 or 𝑥 ≥ 1.9}, where 𝑥 is the value of a single draw of the random variable 𝑋, then the probability of Type-I error is (A) 0.2 (B) 0.1 (C) 0.05 (D) 0.01 Q.16 Let 𝑋 be a uniformly distributed random variable in [𝑎, 𝑏]. The values of an independently drawn sample of size five from 𝑋 are given by {1.3, 0.8, 9.5, 20.2, 8.2}. Let 𝑎̂ and 𝑏̂ denote the Maximum Likelihood Estimates for the parameters 𝑎 and 𝑏, respectively. Then, (A) 𝑎̂ = 0.8; 𝑏̂ = 20.2 (B) 𝑎̂ = 1.3; 𝑏̂ = 9.5 (C) 𝑎̂ = 1.3; 𝑏̂ = 8.2 (D) 𝑎̂ = 0; 𝑏̂ = 21 EN Page 9 of 34 JAM 2021 Economics (EN) Q.17 There are only two firms in an industry producing a homogenous product and having identical production technology. The cost function of firm 𝑖 is 𝐶𝑖 (𝑞𝑖 ) = 𝑞𝑖 2, for 𝑖 = 1,2; where 𝑞𝑖 is the quantity produced by firm 𝑖. The market demand for the product is 𝑝 = 100 − 𝑞, where 𝑝 is the unit price and 𝑞 = 𝑞1 + 𝑞2 is the aggregate quantity. Assuming the firms are price takers, the competitive equilibrium solution of 𝑝 and 𝑞 in this market is (A) 𝑝 = 80, 𝑞 = 20 (B) 𝑝 = 20, 𝑞 = 80 (C) 200 100 𝑝= ,𝑞 = 3 3 (D) 𝑝 = 50, 𝑞 = 50 EN Page 10 of 34 JAM 2021 Economics (EN) Q.18 An upstream paper mill dumps effluents in a river. The total benefit and total cost to the mill are 𝑇𝐵 = 120𝑄 − 𝑄2 and 𝑇𝐶 = 20𝑄, respectively, where 𝑄 is the amount of output it produces. The environmental cost due to the negative externality is 𝐸𝐶 = 𝑄2. The government wants to impose a production tax of 𝑡 per unit of output on the mill. The value of 𝑡 to achieve the socially optimal level of production is (A) 6 (B) 25 (C) 50 (D) 70 Q.19 Which one of the following statements is NOT correct regarding changes in the occupational structure of the workforce between 1951 and 1991 in India? (A) Proportion of cultivators has increased (B) Proportion of agriculture labour has increased (C) Proportion of those employed in the tertiary sector has increased (D) Proportion of those employed in the primary sector has decreased EN Page 11 of 34 JAM 2021 Economics (EN) Q.20 Let 𝑊 be a subspace of the vector space ℝ3 over the field ℝ spanned by 0 2 ( −1 ) and (−1 ). Which one of the following vectors lies in 𝑊 ? 2 0 (A) 1 ( 1) 1 (B) −1 ( 1) 1 (C) 1 (−1 ) 1 (D) 1 ( 1) −1 EN Page 12 of 34 JAM 2021 Economics (EN) Q.21 Let 𝑓 , 𝑔 ∶ ℝ → ℝ be defined by 𝑓 (𝑥 ) = 𝑥𝑒 −𝑥 and 𝑔(𝑥 ) = 𝑥|𝑥|. Then, on ℝ , (A) both 𝑓 and 𝑔 are convex (B) 𝑓 is convex and 𝑔 is not convex (C) 𝑓 is not quasiconvex and 𝑔 is quasiconvex (D) neither 𝑓 nor 𝑔 is quasiconvex EN Page 13 of 34 JAM 2021 Economics (EN) Q.22 Let ( 𝑥1∗ = 1, 𝑥2∗ = 0, 𝑥3∗ = 2) be an optimal solution of the linear programming problem minimize 𝑥1 + 5𝑥2 + 2𝑥3 subject to 𝑥1 − 𝑥2 ≤ 1 𝑥1 + 𝑥2 + 𝑥3 ≥ 3 𝑥1, 𝑥2 , 𝑥3 ≥ 0. If (𝜆∗1 , 𝜆∗2 ) is an optimal solution of its dual, then (A) 2𝜆1∗ = 3𝜆∗2 (B) 2𝜆1∗ = 𝜆∗2 (C) 𝜆∗1 = 2𝜆∗2 (D) 𝜆∗1 = 𝜆∗2 EN Page 14 of 34 JAM 2021 Economics (EN) Q.23 Let 𝑋 and 𝑌 be two independent random variables with the cumulative distribution functions 3 𝑥 𝐹𝑋 (𝑥) = 1 − ( ) , 𝑥 = 1,2,3, ⋯ 4 2 𝑦 𝐺𝑌 (𝑦) = 1 − ( ) , 𝑦 = 1,2,3, ⋯, 3 respectively. Let 𝑍 = min{𝑋, 𝑌}. Then, the probability 𝑃(𝑍 ≥ 6) is (A) 1 64 (B) 1 32 (C) 63 64 (D) 31 32 EN Page 15 of 34 JAM 2021 Economics (EN) Q.24 Let 𝑋 and 𝑌 be two random variables with the joint probability density function 6𝑥𝑦 if 0 < 𝑦 ≤ √𝑥 ≤ 1 𝑓𝑋,𝑌 (𝑥, 𝑦) = { 0 otherwise. 1 2 Then, the conditional probability 𝑃(𝑌 ≥ │ 𝑋 = ) is 3 3 (A) 1 2 (B) 5 9 (C) 5 6 (D) 3 4 Q25 Which one of the following statements is NOT correct in the context of economic planning in India? (A) In the investment strategy for the Second Five Year Plan, a high priority was accorded to the development of heavy capital goods industries over light industries (B) The sectoral allocation to industry was the highest in the First Five Year Plan (C) Plan Holiday for three years was declared after the Third Five Year Plan (D) In each of the first ten Five Year Plan periods, the average incremental capital- output ratio (ICOR) did not exceed 10 % EN Page 16 of 34 JAM 2021 Economics (EN) Q.26 For any two sets 𝑆1 , 𝑆2 ⊂ ℝ, define the set 𝑆1 − 𝑆2 = { 𝑥 ∈ 𝑆1 , 𝑥 ∉ 𝑆2 }. Let 𝑃 = { 𝑥 ∈ ℝ ∶ 𝑥 2 − 2𝑥 − 3 ≤ 0 } and 𝑄 = { 𝑥 ∈ ℝ ∶ log 5( 1 + 𝑥 2 ) ≤ 1 }. Then, (A) 𝑃 − 𝑄 = [ 2 , 3 ] (B) 𝑄 − 𝑃 = ( 1 , 2 ] (C) 𝑃 − 𝑄 = [−3 , −2 ) (D) 𝑄 − 𝑃 = [− 2 , −1) Q.27 The workforce participation rate of a country is 60%. This country has a population of 100 million of which 6 million are unemployed. The unemployment rate for this country is (A) 2 11 (B) 1 11 (C) 3 50 (D) 1 10 EN Page 17 of 34 JAM 2021 Economics (EN) Q.28 According to John Maynard Keynes, which one of the following statements is correct for a closed economy operating at less than the full employment level of output? (A) Savings determines investment (B) Investment determines savings (C) Changes in the money supply have no impact on output (D) Speculative demand for money is determined by the output level Q.29 A monopolist is facing a downward sloping linear market demand. His variable cost of production is zero. The profit maximizing price will (A) lie in the strictly inelastic region of the demand curve (B) lie in the strictly elastic region of the demand curve (C) be at the unitary elastic point of the demand curve (D) be equal to the marginal cost of production EN Page 18 of 34 JAM 2021 Economics (EN) Q.30 X 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 the crime. The detective’s income is taxed at 10 %. If the above transactions happen in the same year and within the boundary of a country, the contribution of these transactions to GDP (in Rs. lakhs) is (A) 5.5 (B) 5 (C) 10 (D) 4.5 EN Page 19 of 34 JAM 2021 Economics (EN) SECTION - B MULTIPLE SELECT QUESTIONS (MSQ) Q. 31 – Q. 40 Carry TWO marks each. Q.31 An amateur singer has just recorded his first music album with a recording company. The demand for his album is given by 𝑄 = 40000 − 800𝑃, where 𝑄 is the number of albums sold and 𝑃 is the price of each album. Furthermore, per unit cost of producing each album is given by Rs. 8. A profit maximizing recording company has offered the following contract options to the singer (i) 20% of the revenue from the sales of the album (ii) Rs. 2 per album sold (iii) A fixed fee of Rs. 32,000 Which of the following is/are correct? (A) Contract (i) yields the highest payment to the singer (B) Contract (ii) yields the highest payment to the singer (C) Contract (iii) yields the highest payment to the singer (D) Contract (ii) and (iii) yield the same payment to the singer EN Page 20 of 34 JAM 2021 Economics (EN) Q.32 There are two firms in an oligopolistic industry competing in prices and selling a homogenous product. Total cost of production for firm 𝑖 is 𝐶𝑖 (𝑞𝑖 ) = 10𝑞𝑖 , 𝑖 = 1,2; where 𝑞𝑖 is the quantity produced by firm 𝑖. Suppose firm 𝑖 sets price 𝑝𝑖 and firm 𝑗 sets price 𝑝𝑗. The market demand faced by firm 𝑖 is given by 100 − 𝑝𝑖 ; if 𝑝𝑖 < 𝑝𝑗 0; if 𝑝𝑖 > 𝑝𝑗 𝑞𝑖 (𝑝𝑖 , 𝑝𝑗 ) = 100 − 𝑝𝑖 { ; if 𝑝𝑖 = 𝑝𝑗 2 for all 𝑖, 𝑗 = 1,2 and 𝑖 ≠ 𝑗. Price can only take integer values in this market. Nash equilibrium/equilibria is/are given by (A) 𝑝1 = 10, 𝑝2 = 10 (B) 𝑝1 = 12, 𝑝2 = 12 (C) 𝑝1 = 40, 𝑝2 = 40 (D) 𝑝1 = 11, 𝑝2 = 11 EN Page 21 of 34 JAM 2021 Economics (EN) Q.33 Which of the following statements is/are correct about the Indian economy during the colonial period? (A) The average annual growth of per capita income was lower during the period 1920-25 to 1947 than the period 1865 to 1920-25. (B) The colonial administration generated a large amount of revenue from peasants by raising the land revenue. (C) The British brought capital from England for the construction of Railways and passed on the burden of interest on it to the Indian tax payers. (D) Dadabhai Naoroji’s estimates of the drain of wealth from India to England included, among other things, the home charges. Q.34 In the context of Expectations Augmented Phillips Curve (EAPC), which of the following statements is/are correct? (A) An increase in the natural rate of unemployment shifts EAPC to the left. (B) An increase in the expected inflation shifts EAPC up and to the right. (C) If actual unemployment rate equals the natural rate of unemployment, the unanticipated inflation equals zero. (D) As long as actual unemployment rate exceeds the natural rate of unemployment, the actual inflation rate exceeds the expected inflation. EN Page 22 of 34 JAM 2021 Economics (EN) Q.35 𝜋 𝜋 Let 𝑓 be a function defined on (− , ) as 2 2 𝜋 cos ( + |𝑥|) 2 𝑓 (𝑥 ) = 𝜋. sin ( − |𝑥| ) 2 Then, (A) 𝑓 is not continuous at 𝑥 = 0 (B) 𝑓 is continuous but not differentiable at 𝑥 = 0 (C) 𝑓 (𝑥 ) − 𝑓 (0) lim+ = −1 𝑥→0 𝑥 (D) 𝑓 ′ (0) = −1 EN Page 23 of 34 JAM 2021 Economics (EN) Q.36 Let 𝑥 , 𝑦 ∈ ℝ and the matrix 𝑥+𝑦 𝑥−𝑦 𝑀= [ ]. 𝑥−𝑦 𝑥+𝑦 Also, let 𝑎𝑑𝑗(𝑀) be the adjoint and det(𝑀) be the determinant of the matrix 𝑀. 3 −1 If 𝑀 [ ]= [ ] , then 1 3 (A) 3 𝑥+𝑦 = − 4 (B) 3 𝑥− 𝑦 = 4 (C) det(𝑀) = −1 (D) det( 𝑎𝑑𝑗(𝑀)) = 1 EN Page 24 of 34 JAM 2021 Economics (EN) Q.37 The net inflow of foreign currency into a country on current account and capital account combined is negative in a particular year. The country could be following a fixed or a flexible exchange rate regime. Which of the following scenarios is/are possible for the country’s economy in that year? (A) The country’s foreign exchange reserves may increase (B) The country’s exchange rate may appreciate (C) The country’s foreign exchange reserves may decrease (D) The country’s exchange rate may depreciate Q.38 Let 𝑘 ∈ ℝ. Which of the following statements is/are correct for the roots of the quadratic equation 𝑥 2 + 2 (𝑘 + 1)𝑥 + 9𝑘 − 5 = 0 (A) If 𝑘 ≤ 1 , then the roots are real and positive (B) If 2 ≤ 𝑘 ≤ 4 , then the roots are complex (C) If 4 < 𝑘 < 6 , then the roots are real and opposite in sign (D) If 𝑘 ≥ 6 , then the roots are real and negative EN Page 25 of 34 JAM 2021 Economics (EN) Q.39 If the number of employed workers in a country increases while its population does not change, then the unemployment rate in the country (A) will always increase (B) will always decrease (C) may increase (D) may decrease Q.40 There are two sellers, 𝐻 and 𝐿, in a second-hand goods market where product quality varies. The sellers know the quality of their own product but the buyers cannot distinguish the product quality without further information. Sellers’ valuation of their own product is based on the quality. 𝐻 is willing to sell his product with quality 𝑄𝐻 at a price 𝑃𝐻 per unit and 𝐿 is willing to sell the product with quality 𝑄𝐿 at a price 𝑃𝐿 per unit such that 𝑄𝐻 > 𝑄𝐿 and 𝑃𝐻 > 𝑃𝐿. This market will suffer from (A) adverse selection (B) moral hazard (C) market failure (D) excess supply EN Page 26 of 34 JAM 2021 Economics (EN) SECTION – C NUMERICAL ANSWER TYPE (NAT) Q. 41 – Q. 50 Carry ONE mark each. Q.41 The amount of money a gambler can win in a casino is determined by three independent rolls of a six-faced fair dice. The gambler wins Rs. 800 if he gets three sixes, Rs. 400 if he gets two sixes, and Rs. 100 in the event of getting only one six. The gambler does not win or lose any money in all other possible outcomes. The probability that a gambler will win at least Rs. 100 is ___________. (round off to 2 decimal places) Q.42 Consider an economy where the full employment output is 1 trillion Rupees and the natural rate of unemployment is 6 %. If actual unemployment rate is 8 %, then according to Okun’s law, the absolute gap between the full employment output and actual output (in billion Rupees) will be ___________. (in integer) Q.43 The values of normalized indices for a country are as follows. Dimension Value of normalized index Standard of living 0.4 Education 0.2 Health 0.8 Following the current UNDP methodology, the value of Human Development Index (HDI) for the country is _______________. (round off to 1 decimal place) EN Page 27 of 34 JAM 2021 Economics (EN) Q.44 The value of the integral 9 𝑥−1 ∫ 𝑑𝑥 0 1 + √𝑥 is _____________. (in integer) Q.45 Consider the first order difference equation 𝑛+1 𝑥𝑛 = ( ) 𝑥𝑛−1 , 𝑛 = 1, 2, 3, … 𝑛 If 𝑥0 = 2 , then 𝑥100 − 𝑥50 equals _____________. (in integer) Q.46 In a small open economy, the desired domestic savings ( 𝑆 𝑑 ) and the desired domestic investment ( 𝐼 𝑑 ) are as follows, where 𝑟 𝑤 is the world real interest rate. 𝑆 𝑑 = 10 + 100 𝑟 𝑤 𝐼 𝑑 = 15 − 100 𝑟 𝑤 If 𝑟 𝑤 = 3 %, the current account balance in the equilibrium would be ________________. (in integer) EN Page 28 of 34 JAM 2021 Economics (EN) Q.47 Let 𝑋1 ~ 𝑁(𝜇1 , 𝜎12 ) and 𝑋2 ∼ 𝑁(𝜇2 , 𝜎22 ) be two normally distributed random variables, where 𝜇1 = 2, 𝜇2 = 3 and 𝜎12 = 4, 𝜎22 = 9. The correlation coefficient between them is 0.5. The variance of the random variable (𝑋1 + 𝑋2 ) is ________________. (in integer) Q.48 A consumer always spends 50% of his monthly income on food. Introduction of value added tax on food items has led to a 20% increase in food prices while his monthly income remained unchanged. The consumer’s price elasticity of demand for food is _________________. (in integer) Q.49 The utility function of a consumer from consumption of 𝑥1 and 𝑥2 is given by 𝑢(𝑥1 , 𝑥2 ) = 𝑥1 + 2√𝑥2. At the current prices and income, the consumer’s optimal consumption bundle is given by (𝑥1 = 10, 𝑥2 = 10). The consumer’s optimal choice of 𝑥2 , if his income increases by 50% but prices remain unchanged, is ___________. (in integer) EN Page 29 of 34 JAM 2021 Economics (EN) Q.50 The following data relate to a country’s GDP in 2012-13 (in local currency). Item Value GDP 59,816 Private sector investment 17,811 Exports 14,498 Investment expenditure by the government 5,087 Net Factor Income from Abroad 125 Consumption expenditure by the government 6,620 Private sector consumption 35,695 The value of this country’s imports (in local currency) in 2012-13 is _______________. (in integer) EN Page 30 of 34 JAM 2021 Economics (EN) Q. 51 – Q. 60 Carry TWO mark each. Q.51 Amar has an endowment of food 𝐹𝐴 = 2 and water 𝑊𝐴 = 5. Barun has an endowment of food 𝐹𝐵 = 8 and water 𝑊𝐵 = 5. Amar’s utility function is given by 𝑈𝐴 (𝑓𝐴 , 𝑤𝐴 ) = 𝑓𝐴2 𝑤𝐴 ; where 𝑓𝐴 and 𝑤𝐴 are his consumption of food and water, respectively. Barun’s utility function is given by 𝑈𝐵 (𝑓𝐵 , 𝑤𝐵 ) = min {𝑓𝐵 , 𝑤𝐵 }; where 𝑓𝐵 and 𝑤𝐵 are his consumption of food and water, respectively. They exchange food and water at prices 𝑝𝑓 and 𝑝𝑤 , respectively, to maximize their 𝑝𝑓 utilities. In the competitive equilibrium, equals _______________. (in 𝑝𝑤 integer) Q.52 The supply and demand curves of a vaccine are 𝑞 = 14 + 5𝑝 and 𝑞 = 329 − 5𝑝, respectively, where 𝑝 is price per unit of vaccine and 𝑞 is quantity of vaccine. The government decides that the maximum price of the vaccine would be Rs. 25 per unit. To avoid any shortage in supply at the ceiling price, the government also decides to subsidize the sellers so that the market clears. Subsidy is given on per unit basis. The total expenditure of the government in providing the subsidy is Rs. __________________. (in integer) EN Page 31 of 34 JAM 2021 Economics (EN) Q.53 A firm has two manufacturing plants, 1 and 2 to produce the same product. The total costs of production are given by 𝑇𝐶1 = 500 + 30𝑄1 and 𝑇𝐶2 = 1500 + 20𝑄2 in plants 1 and 2, respectively, where 𝑄1 and 𝑄2 are the respective quantities. 𝑃 The demand for the product is given by 𝑄 𝑑 = 150 − , where 𝑃 is the 3 price per unit. The value of 𝑄1 that maximizes the profit of the firm is __________. (in integer) Q.54 Let 𝑦 (𝑥 ) > 0 be a solution of the differential equation 𝑑𝑦 + 𝑦 = 𝑦2. 𝑑𝑥 1 If 𝑦( ln 2 ) = , where ln denotes the natural logarithmic function, then 3 𝑦( ln 3 ) equals __________________. (round off to 2 decimal places) Q.55 The optimal value of the constrained optimization problem minimize 2𝑥𝑦 subject to 9𝑥 2 + 4𝑦 2 ≤ 36 is _________________. (in integer) EN Page 32 of 34 JAM 2021 Economics (EN) Q.56 For some 𝛽 > 0, let the variables 𝑥1 and 𝑥3 be the optimal basic feasible solution of the linear programming problem maximize 𝑥1 + 2𝑥2 + 3𝑥3 subject to 2𝑥1 − 𝑥2 + 𝑥3 = 9 𝑥1 + 2 𝑥2 − 𝛽𝑥3 = 1 𝑥1 , 𝑥2 , 𝑥3 ≥ 0. If the optimal value is 7, then 𝛽 equals ________________. (in integer) Q.57 Let 𝑋1 , 𝑋2 , 𝑋3 , 𝑋4 be independent random variables following the standard normal distribution. Let 𝑌 be defined as, 𝑌 = (𝑋1 + 𝑋2 )2 + (𝑋3 + 𝑋4 )2. Then the variance of 𝑌 equals __________. (in integer) Q.58 The aggregate production function for a country is, 𝑌 = 10𝑁 − 0.005𝑁 2 , where 𝑁 is the quantity of labor input. The aggregate labor supply function is 𝑁 = 55 + 5𝑤 , where 𝑤 is the real wage rate. Assuming perfectly competitive labor and product markets, the equilibrium real wage is _______________. (in integer) Q.59 Individuals in a country start earning and consuming at the age of 18 years, retire at the age of 60 years and die at the age of 90 years, without leaving any debt and bequests. The income of an individual at age 𝑡 (in years) is given by the expression 100𝑡 − 𝑡 2. The price level is constant and the interest rate is zero. According to the life cycle theory of consumption, the average annual consumption of an individual is ________________. (in integer) EN Page 33 of 34 JAM 2021 Economics (EN) Q.60 The IS-LM model for a closed economy is given below, where 𝑌 is the output, 𝐶 is the consumption, 𝐼 is the investment, 𝑇 is the income tax, 𝑀 𝑑 is the money demand, 𝑃 is the price level, 𝑟 is the real interest rate, 𝜋 𝑒 is expected inflation rate and 𝐺 is the government expenditure. 𝐶 = 200 + 0.8 (𝑌 − 𝑇) − 500 𝑟 𝐼 = 200 − 500 𝑟 𝑇 = 20 + 0.25 𝑌 𝑀𝑑 = 0.5 𝑌 − 250 (𝑟 + 𝜋 𝑒 ) 𝑃 If 𝐺 = 196 , 𝜋 𝑒 = 0.1 , the nominal money supply equals 9890 and the full employment output equals 1000, the full employment equilibrium price level in the economy is ________________. (in integer) END OF THE QUESTION PAPER EN Page 34 of 34