IIT JAM 2022 Economics (EN) Question Paper with Answer Key pdf is available for download. The exam was conducted by IIT Roorkee on February 13, 2022. In terms of difficulty level, IIT JAM Economics (EN) was of Easy to Moderate level. The question paper comprised a total of 60 questions.
IIT JAM 2022 Economics (EN) Question Paper with Answer Key PDFs
| IIT JAM 2022 Economics (EN) Question Paper with Answer Key PDFs | Download PDF | Check Solutions |
When the supply curve \( S_x \) is backward bending and the demand curve \( D_x \) is downward sloping as shown in the figure, there are two equilibria \( M \) and \( N \), respectively. Which of the following statements is CORRECT?
Which of the following deficits indicates the true current fiscal position of the Indian Economy?
Which of the following CORRECTLY defines the relationship between the variances of sample means for simple random samples drawn with and without replacement from a normal population?
Suppose that one million unemployed persons in a country are receiving Rs. 6000 per month per person as an unemployment allowance. If the government, instead of paying unemployment allowance, hires all of them at the same amount (Rs. 6000 per month per person) and engages them in digging the pits and filling the same pits. What will be the effect on GDP?
Which amendments to the constitution have provided constitutional status to the rural and urban local bodies in India?
Let \( W \) be a subspace of a vector space \( \mathbb{R}^3 \). Then, which of the following sets of vectors forms a basis of \( W \)?
From the following, who first examined the close negative relationship between the unemployment rate and the output ratio?
In hypothesis testing, which of the following defines the size of power of the test?
Which of the following is NOT a postulate of the Classical Model of full-employment equilibrium?
A long-run cost function for a product exhibits economies of scale if
Let \( x^2 + 3y^2 = 4 \) for all \( x, y \in \mathbb{R} \), \( y' = \frac{dy}{dx} \), and \( y'' = \frac{d^2y}{dx^2} \). Then
Match List I with List II and choose the CORRECT option.
Let \( f: [0, \infty) \to \mathbb{R} \) be a function defined by \( f(x) = \frac{x + 1}{x + 2} \) for all \( x \in \mathbb{R} \). Then \( f \) is
An economy is characterized by the Solow model, with the production function \( y = \sqrt{k} \), where \( y \) is output per worker and \( k \) is capital per worker. The steady-state level of output per worker is \[ y^{ss} = A^{\frac{1}{1-\alpha}} \left( \frac{y}{k} \right)^{\frac{\alpha}{1-\alpha}}, \]
where \( A \), \( \gamma \), \( \delta \), and \( \alpha \) denote productivity, share of output invested (in %), depreciation rate (in %), and capital’s share in income (in fraction), respectively. Suppose that \( A = 1 \), \( k = 400 \), \( \gamma = 50% \), \( \delta = 5% \) and \( \alpha = 1/2 \). Then the current output, using the above information, is
Which of the following is NOT related to the structural adjustment programmes implemented in India after 1991?
Let a second order difference equation be \[ y_{n+2} + 4y_{n+1} = 4y_n, \quad n = 2, 3, 4, \dots, \quad y_0 = 1, \quad y_1 = 4. \]
Then the general solution is
Suppose that two random samples of sizes \( n_1 \) and \( n_2 \) are selected without replacement from two binomial populations with means \( \mu_1 = n_1 p_1 \), \( \mu_2 = n_2 p_2 \) and variances \( \sigma_1^2 = n_1 p_1 q_1 \), \( \sigma_2^2 = n_2 p_2 q_2 \), respectively. Let the difference of sample proportions \( \overline{P_1} \) and \( \overline{P_2} \) approximate a normal distribution with mean \( p_1 - p_2 \). Then the standard deviation of the difference of sample proportions \( \overline{P_1} \) and \( \overline{P_2} \) is
Which of the following statements is NOT correct in the context of quantity theory of money?
Let the function \( f: \mathbb{R}^2 \to \mathbb{R} \) be \[ f(x, y) = \frac{x y^2}{x^2 + 2x y + y^3}, \quad f(0, 0) = 0. \]
Then
Which of the following measures was announced by the Government of India in the year 1994?
An analyst at the Green Car Co. Ltd. estimated the following demand function for the electric vehicles it sells: \[ Q_E = 0.75 - 1.5P_E + 2.5P_F - 0.5P_B + 3.2I \]
where \( Q_E \) = Number of electric vehicles (in thousand per year), \( P_E \) = Unit price of electric vehicle (Rs. in Lakh), \( P_F \) = Average unit price of vehicle using fossil fuels (Rs. in Lakh), \( P_B \) = Unit price of battery used in electric vehicle (Rs. in Lakh), \( I \) = Personal disposable income (Rs. in Lakh). Let \( P_E = 6.5 \) Lakh, \( P_F = 4.5 \) Lakh, \( P_B = 0.5 \) Lakh and \( I = 10 \) Lakh. Then the income elasticity of demand \( (\varepsilon_{Q_EI}) \) and the cross price elasticity of demand \( (\varepsilon_{Q_E P_F}) \) satisfy
Choose the option that represents the original linear programming problem based on the initial simplex tableau given below, where \( S_i \) represents slack/surplus variables and \( A_i \) represents the artificial variables corresponding to the \( i \)-th constraint:
Let a production function be given by \[ \log Q = \frac{\beta}{\alpha} \log (L^\alpha + K^\beta), \quad where \quad \alpha \in (-\infty, 1] - \{0\} \quad and \quad \beta > 0. \]
Then identify the statement that is NOT correct.
View Solution
Step 1: Understanding the production function.
The given production function involves both \( L \) (labor) and \( K \) (capital), with the parameters \( \alpha \) and \( \beta \). The returns to scale can be analyzed by examining the sum of the exponents in the production function.
Step 2: Identifying returns to scale.
The returns to scale depend on the sum of the exponents \( \alpha \) and \( \beta \). If \( \beta > 1 \), the function exhibits increasing returns to scale, and if \( \beta < 1 \), the function exhibits decreasing returns to scale. The ratio \( \frac{\beta}{\alpha} \) is used to identify these factors.
Step 3: Elasticity of substitution.
The elasticity of substitution in a Cobb-Douglas function is given by \( \frac{1}{1 - \alpha} \), which is true for the given function. The elasticity of substitution cannot be expressed as \( \frac{1}{1 - \beta} \), so option (D) is incorrect.
Step 4: Conclusion.
Thus, the correct answer is (D).
Quick Tip: The elasticity of substitution in production functions often depends on the exponents of labor and capital. In this case, it is based on \( \alpha \), not \( \beta \).
Which of the following statements is NOT correct under the IS-LM (Fixed Price) model?
The probability of getting head in a toss of a biased coin is \( \frac{2}{3} \). Let the coin be tossed three times independently. Then the probability of getting head in the first two tosses and tail in the final toss is
Consider a pure exchange economy with two goods \( x \) and \( y \). Ravi and Suraj are two individuals with utility functions \( U_R = \beta \log(xy) \) and \( U_S = \left( \frac{x_S}{y_S} \right)^\alpha \), respectively. The endowments are \( x_R \) and \( y_R \) for Ravi and \( x_S \) and \( y_S \) for Suraj such that \( x_R + x_S = A \) and \( y_R + y_S = B \). Then their contract curve is
Which of the following is NOT correct regarding \( R^2 \) and Adjusted \( R^2 \)?
The technical change in the endogenous growth model is endogenized by
Which of the following statements is CORRECT for Game A and Game B?
The short-run production function of a firm is \( Q = 200 + 0.21L^2 - 0.0004L^3 \). If wage rate equals Rs. 140 and the number of labors (\( L \)) is 100, then the Marginal Cost and the Average Variable Cost, respectively, are
Let \( X \sim N(\mu_X, \sigma_X^2) \) and \( Y \sim N(\mu_Y, \sigma_Y^2) \). Which of the following is/are NOT correct?
Matching List I and List II, choose the CORRECT option(s).
Suppose that the regression model is \( Y_i = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \mu_i, \, i = 1, 2, \dots, n \). Which of the following null hypotheses could be tested using the F-test?
Let \( f(x) = |x| + \cos\left( \frac{\pi}{2} - x \right) \), where \( x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \). Then
View Solution
Step 1: Continuity and differentiability of \( f(x) \).
The function \( f(x) = |x| + \cos\left( \frac{\pi}{2} - x \right) \) is continuous everywhere in the interval \( \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \) except at \( x = 0 \), where the absolute value function causes a cusp. Thus, the function is not differentiable at \( x = 0 \).
Step 2: Conclusion.
The correct answer is (C).
Quick Tip: A function that is continuous but has a sharp corner (such as the absolute value function at zero) is not differentiable at that point.
The real exchange rate is given by \( e = \frac{EP}{P^*} \), where \( e \) is the price of domestic goods in terms of foreign goods, \( E \) is the price of domestic currency in terms of foreign currency, \( P \) is the domestic price level, and \( P^* \) is the foreign price level. If the Indian Rupee depreciates vis-à-vis the Japanese Yen, and the Marshall-Lerner condition holds, then
The demand function \( (Q^D_x) \) and supply function \( (Q^S_x) \) are given as: \[ Q^D_x = f(P_x, I) \quad and \quad Q^S_x = g(P_x, A) \]
where \( I \) (Income) and \( A \) (Advertisement expenses) are the exogenous factors affecting quantity demanded and supplied, respectively. Further, \[ \frac{\partial f{\partial P_x} \leq 0, \quad \frac{\partial g}{\partial P_x} > 0 \quad and \quad \frac{\partial f}{\partial I} > 0 \]
and \[ \frac{\partial g{\partial A} may have any sign. Considering that there exists an equilibrium \( (Q^D_x = Q^S_x = Q) \), which of the following is/are CORRECT? \]
Which of the following statements is/are CORRECT under the Keynesian Cross (Fixed Price) Model?
Which of the following functions is/are homogeneous?
In the context of Indian agriculture, which of the following statements is/are CORRECT?
Let a monopolist demand curve be given by \( Q = P^e \), where \( Q \) is output, \( P \) is price, \( e \) is the price elasticity of demand \( (e < -1) \), and Marginal Cost = Average Cost = \( \alpha \). If \( P_C \) and \( P_M \) represent the price under perfect competition and monopoly, respectively, then which of the following is/are NOT correct? (CS_M and CS_C represent the consumer surplus under monopoly and perfect competition, respectively.)
The sum of the eigen values of the square matrix 
is _____ \text{(in integer).
Monthly per capita consumption expenditure (MPCE) of 10 households in a region is given below.
Assuming the poverty cutoff (Z) of MPCE to be Rs. 2000, the squared poverty gap ratio is _____ \text{(round off to 3 decimal places).
Suppose that the full employment level of output of an economy is Rs. 2200 million, expenditure determined level of output is Rs. 2163 million, and the marginal propensity to consume is 0.75. The deflationary gap equals Rs. _____ \text{million (round off to 2 decimal places).
Let \( a, b \in \mathbb{R} \). If \( f(x) = ax + b \) is such that \[ a + b = 4 \quad and \quad f(x + y) = f(x) + f(y) - 2 \quad for all \, x, y \in \mathbb{R}, \]
then \[ \sum_{n=1}^{\infty} f(n) = \_\_\_\_\_ \, (in integer). \]
The Total Variable Cost (TVC) for a firm is given by \[ TVC = x^3 - bx^2. \]
The Total Fixed Cost is 848. The value of \( b \) for which the Marginal Cost is minimum at \( x = 16 \) is _____ \, \text{(in integer).
Let the consumption function, tax function, and income identity be given by \[ C = C_0 + b(Y - T), \quad T = T_0 + tY, \quad Y = C + I_0 + G_0, \]
respectively, where \( C_0, I_0, G_0, T_0 \) are autonomous consumption, investment, government expenditure, and tax, respectively. If \( b = 0.75 \) and \( t = 0.1 \), then an increase in \( G_0 \) by Rs. 20 million will increase \( Y \) by Rs. _____ \, \text{million (round off to 2 decimal places).
Let the system of equations be \( \alpha u + v = 0 \), \( u + \alpha v = 0 \), \( v + \alpha w = 0 \), where \( \alpha \in \mathbb{R} \). Then the system has infinite solutions if \( \alpha = \) ....... (in integer).
Assume that the cost function for the \( i \)-th firm in an industry is given by
\( C_i = 0.25q_i^2 + 2q_i + 5 \), \( i = 1, 2, \dots, 150 \),
where \( C_i \) and \( q_i \) are cost and output for the \( i \)-th firm, respectively.
Let the aggregate inverse demand function be
\( P = 10 - 0.01Q \), where \( P \) is the unit price and \( Q \) is the aggregate output.
Assuming perfect competition, the equilibrium quantity is ............ (in integer).
The following table presents the national income related aggregates (at current prices) for the year 2019-20:
The personal disposable income for the year 2019-20 is Rs. ............. Lakh Crores (in integer).
The following table provides a list of countries selling Big Mac and market exchange rates in January 2019:
Using the above information, the cheapest price (in USD) of Big Mac is ............... (round off to 2 decimal places).
An individual faces an uncertain prospect, where wealth could be Rs. 10 Lakh with probability 0.75 and Rs. 7 Lakh with probability 0.25.
Let the utility function be \( U(w) = w^3 \). Then the individual will buy full insurance by paying a premium of Rs. ........... Lakh (round off to 2 decimal places).
Suppose that per capita GDP of India and USA are growing at annual average rates of 8.8% and 1.8%, respectively. Further, consider that in 2019-20, per capita GDP of USA was USD 41099 and per capita GDP of India was USD 1570. Assuming that the two countries continue to grow at the above rates, India’s per capita GDP will be equal to the per capita GDP of USA in ........... years (round off to 2 decimal places).
If \[ \int \log\left( 1 + \frac{2}{t} \right) dt = g(t) \left( \frac{t^2}{2} - 2 \right) + f(t) \cdot \frac{t^2}{2} + Kt + C, \]
where \( C \) is an arbitrary constant, then 2K is .............. (in integer).
ACD Bank holds a total deposit of Rs. 256412. To expand the money supply in the economy during the COVID-19 pandemic period, the Reserve Bank of India reduces the cash reserve ratio (CRR) from 4.5% to 3.5%. Due to this policy change, the additional money supply generated by ACD Bank is Rs. ............. (in integer).
Suppose that the regression model is \[ Y_{n \times 1} = X_{n \times 3} \beta_{3 \times 1} + U_{n \times 1} \]
with \[ \beta_{3 \times 1} = \begin{bmatrix} \beta_1
\beta_2
\beta_3 \end{bmatrix}. \]
A random sample of size \( n = 23 \) on \( Y \) and \( X \) is drawn from the normal population. Using the data, if a researcher obtains
where \( e \) denotes the vector of estimated residuals, then the t-statistic to test the null hypothesis \( \beta_3 = 0 \) is ............ (round off to 2 decimal places).
View Solution
Step 1: Formula for the t-statistic.
The t-statistic for testing \( \beta_3 = 0 \) is given by: \[ t = \frac{\hat{\beta}_3}{Standard Error of \hat{\beta}_3} \]
The standard error is given by: \[ SE(\hat{\beta}_3) = \sqrt{\frac{e^T e}{n - k} \cdot \left( (X^T X)^{-1} \right)_{33}}, \]
where \( k = 3 \) is the number of predictors.
Step 2: Calculate \( \hat{\beta}_3 \).
Step 3: Calculate the standard error.
Substitute into the formula: \[ SE(\hat{\beta}_3) = \sqrt{\frac{0.7}{23 - 3} \cdot 0.3} = \sqrt{\frac{0.7}{20} \cdot 0.3} \approx 0.132. \]
Step 4: Calculate the t-statistic.
Now, calculate the t-statistic: \[ t = \frac{0.1}{0.132} \approx 0.76 \]
Step 5: Conclusion.
The t-statistic to test the null hypothesis \( \beta_3 = 0 \) is approximately 0.76.
Final Answer: \[ \boxed{0.76} \] Quick Tip: The t-statistic for hypothesis testing of regression coefficients is the estimated coefficient divided by its standard error.
Given the production function \[ Q = 6 \sqrt{L}, \]
and the supply of labour \[ L = \sqrt{w}, \]
where \( L \) and \( w \) denote the number of labours and wage rate, respectively. If the unit price of the product is Rs. 243, then the profit-maximizing value of \( w \) is Rs. .......... (in integer).
Given the following information related to product and money markets,
Product Market: \[ C = 300 + 0.8(Y - T) \quad T = 200 + 0.2(Y) \quad I_0 = 300; G_0 = 400 \]
Money Market: \[ \frac{M_0}{P} = 0.4Y - 200i \quad M_0 = 900; P = 1 (Fixed) \]
where \( Y = \) Income, \( C = \) Consumption, \( T = \) Tax, \( I_0 = \) Autonomous Investment, \( G_0 = \) Autonomous Government Expenditure, \( M_0 = \) Nominal Money Demand, \( P = \) Price, and \( i = \) Interest Rate.
The equilibrium level of interest rate (in %) is ............ (round off to 2 decimal places).
Let the linear programming problem be \[ Maximize \quad Z = 0.2x_1 + x_2 \]
subject to \[ 2x_1 + 5x_2 \leq 70, \quad x_1 + x_2 \leq 20, \quad x_1, x_2 \geq 0 \]
If \( x_1 = a \) and \( x_2 = b \) is the optimal solution, then \( a + b = \) ................ (in integer).
Let the production function be \[ Q = \sqrt{L^2 + K^2}, \]
the unit price of labour (\( L \)) and capital (\( K \)) be Rs. 30 and Rs. 40, respectively, and the total cost be Rs. 580. Then the maximum value of \( Q \) subject to the cost constraint is __________ (round off to 2 decimal places).
In a market, two firms \( F_1 \) and \( F_2 \) are producing homogenous products. The inverse demand function is given by \[ p = 120 - 0.5(q_1 + q_2), \]
where \( p \) is the unit price of the product, and \( q_1 \) and \( q_2 \) are the outputs from \( F_1 \) and \( F_2 \), respectively. Suppose the cost functions of \( F_1 \) and \( F_2 \) are
\[
C_1 = 20q_1 \quad \text{and \quad C_2 = 10 + 0.5q_2^2, \quad \text{respectively. Then the total profit earned by both the firms assuming a competitive situation is __________ (in integer).
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