List of top Questions asked in IIT JAM EN- 2021

The IS–LM model for a closed economy is given below, where $Y$ is output, $C$ is consumption, $I$ is investment, $T$ is income tax, $\dfrac{M^d}{P}$ is money demand, $P$ is price level, $r$ is real interest rate, $\pi^e$ is expected inflation rate and $G$ is government expenditure: \[ C = 200 + 0.8(Y - T) - 500r, \] \[ I = 200 - 500r, \] \[ T = 20 + 0.25Y, \] \[ \frac{M^d}{P} = 0.5Y - 250(r + \pi^e). \] If $G = 196$, $\pi^e = 0.1$, 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) 
 

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) 
 

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) 
 

Let $X_1, X_2, X_3, X_4$ be independent random variables following the standard normal distribution. Let $Y$ be defined as \[ Y = (X_1 + X_2)^2 + (X_3 + X_4)^2. \] Then the variance of $Y$ equals __________. (in integer) 
 

For $\beta>0$, let the variables $x_1$ and $x_3$ be the optimal basic feasible solution of the linear programming problem \[ \text{maximize } \; z = x_1 + 2x_2 + 3x_3 \] 

If the optimal value is 7, then $\beta$ equals ____________. (in integer) 
 

The optimal value of the constrained optimization problem \[ \text{minimize } 2xy \quad \text{subject to } 9x^2 + 4y^2 \leq 36 \] is _____________. (in integer) 
 

The supply and demand curves of a vaccine are \[ q = 14 + 5p \quad \text{and} \quad q = 329 - 5p, \] respectively, where $p$ is the 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) 
 

The following data relate to a country’s GDP in 2012–13 (in local currency). 

The value of this country’s imports (in local currency) in 2012–13 is __________. (in integer) 
 

The utility function of a consumer from consumption of $x_1$ and $x_2$ is given by \[ u(x_1, x_2) = x_1 + 2\sqrt{x_2}. \] At the current prices and income, the consumer’s optimal consumption bundle is given by $(x_1 = 10, x_2 = 10)$. The consumer’s optimal choice of $x_2$, if his income increases by 50% but prices remain unchanged, is __________. (in integer) 
 

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) 
 

Let $X_1 \sim N(\mu_1, \sigma_1^2)$ and $X_2 \sim N(\mu_2, \sigma_2^2)$ be two normally distributed random variables, where $\mu_1 = 2, \mu_2 = 3$ and $\sigma_1^2 = 4, \sigma_2^2 = 9$. The correlation coefficient between them is 0.5. The variance of the random variable $(X_1 + X_2)$ is ___________. (in integer) 
 

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. \[ S^d = 10 + 100r^w, \quad I^d = 15 - 100r^w \] If $r^w = 3%$, the current account balance in the equilibrium would be ___________. (in integer) 
 

The value of the integral \[ \int_{0}^{9} \frac{x - 1}{1 + \sqrt{x}} \, dx \] is _____________. (in integer) 
 

The values of normalized indices for a country are as follows. 

Following the current UNDP methodology, the value of Human Development Index (HDI) for the country is __________. (round off to 1 decimal place) 
 

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. 400 is ___________. (round off to 2 decimal places) 
 

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)