DSE 2012 question paper

All 60 questions from the DSE 2012 Delhi School of Economics MA entrance paper. Open any question for the worked solution.

Q1A rural landowner can deposit his savings in a commercial bank and receive an annual interest rate of 8%. Alternatively he can lend to villagers who…
Q2Consider a two-person two-good exchange economy, where agents are denoted by A,B and goods are denoted by X,Y. A Pareto optimal allocation of this…
Q3Given the same production function and market demand, a monopolist earns at least as much profit as a competitive firm in the short run, because
Q4Mr. B thinks cheese is addictive, the more you eat, the more you want. Suppose x denotes the quantity of cheese. Mr. B's utility function can be…
Q5Sania and Saina are bargaining over how to split 10 Rupees. Both claimants simultaneously name shares they would like to have, s₁ and s₂, where 0≤…
Q6\"Developing new antibiotics is expensive. It is also known that the more frequently bacteria are exposed to antibiotics, the more quickly the…
Q7If the correlation between variables X and Y is 0, then
Q8One reason why the sample median is used as an estimator of the population mean is that
Q9Suppose X is a random variable, which follows Uniform[-1,1]. Find the covariance between X and X².
Q10Which of the following statements is not an indicator that multicollinearity among two or more variables is present in a multiple regression model…
Q11Given the linear regression Y=α+β X; a very high correlation between variables X and Y necessarily implies that
Q12What would happen (other things being equal) to a confidence interval if you calculated a 99% confidence interval rather than a 95% confidence…
Q13An n -gon is a regular polygon with n equal sides. Find the number of diagonals (edges of an n -gon are not considered as diagonals) of a 10 -gon.
Q14∫₀¹ xⁿsin (x) dx
Q15lim_(n→∞)(√((n-1))-√n)
Q16The equation x⁷=x+1
Q17The cumulative distribution function F(x) of a random variable has a slope of 1 for x in the interval [0,1] and takes a constant value thereafter.…
Q18A and B are two non empty sets. A-B={x∈ A| x∉ B} and A+B=(A-B)∪(B-A). Consider the following statements; Statement 1: A+B=B implies A⊆ B. Statement…
Q19The short-run aggregate supply curve is upward sloping because
Q20The investment demand curve shifts rightward if
Q21A firm producing hockey sticks in Punjab has a production function given by Q=2√KL where K stands for capital, L stands for labour and Q stands for…
Q22Antony and Cleopatra run a food stall together. Their joint profit is 10 Rupees per month, from which Antony gets I_A Rupees and Cleopatra gets I_C…
Q23Consider a homogenous goods market with the demand function Q=30-P. There are two firms playing a price game in the following manner: firm 1 quotes…
Q24Consider the following two-player game. The players simultaneously draw one sample each from a continuous random variable X, which follows…
Q25The productivity of a labourer depends on his daily wage. In some range of wage, the more he is paid, the better his health and the more work he is…
Q26Consider a society in which half the population earns 100 rupees per day and the other half earns 200 rupees per day. The Gini coefficient of…
Q27A and B live in an exchange economy. There are two goods X and Y. Utility functions of A and B are U^A(x,y)=x+y and U^B(x,y)=x²+y², respectively. A…
Q28Fill in the blanks: Given a downward sloping linear demand curve and constant marginal cost curves, if a per unit tax is imposed on a monopoly, a…
Q29The demand curve for electricity is D(p)=120-p. The marginal cost of electricity production is MC₁(q)=20+q. The marginal cost of pollution due to…
Q30Suppose that there are two agents in an economy with income x₁ and x₂. If the richer person transfers a portion of her income to the poorer person…
Q31Consider the following model, estimated using OLS Yᵢ=β Xᵢ+εᵢ; i=1,2,...,n where there is no intercept, and Var(εᵢ)=σ². Which of the following…
Q32An analyst trying to estimate the demand for rice has estimated the following two models. Model 1: D=50+0.3Y+0.1P+12N; R²=0.7, where D is the demand…
Q33Consider the regressions Yᵢ*=β̂₁*+β̂₂*Xᵢ*+ûᵢ*, and Yᵢ=β̂₁+β̂₂Xᵢ+ûᵢ, where Yᵢ*=w₁Yᵢ and Xᵢ*=w₂Xᵢ; w₁,w₂ are constants. Is it true that
Q34For variables X and Y we have the data Σ XY=350, Σ X=50, Σ Y=60, X̅=5, σ_X²=4, σ_Y²=9 where X̅ denotes the mean of X and σ_X² denotes the variance…
Q35X is a normally distributed random variable with unknown mean μ and standard deviation equal to 2. The value of the sample mean from a random sample…
Q36An econometrician uses data from the Consumer Expenditure Survey conducted by the National Sample Survey Organization for the years 1991 and 2001…
Q37Let X₁,X₂,…,Xₙ be random samples from a normal distribution with parameters μ and σ². Then the random variable ((n-1)S²)/σ²=1/σ²Σᵢ₌₁ⁿ(Xᵢ-X̅)² has a…
Q38Suppose you have 500 observations and you regress wage (measured in rupees per hour) on experience in the labour market, exper (measures in years)…
Q39Suppose you have a sample of size one from one of the following densities H₀: f(x)=2x, 0≤ x≤ 1 and H₁: f(x)=2-2x, 0≤ x≤ 1. Let α and β denote type I…
Q40An urn contains equal number of green and red balls. Suppose you are playing the following game. You draw one ball at random from the urn and note…
Q41Two women and four men are to be seated randomly around a circular table. Find the probability that the women are not seated next to each other.
Q42A fair coin is tossed until a head comes up for the first time. The probability of this happening on an odd-numbered toss is
Q43An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, then the number of…
Q44Consider the system of equations α x+β y=0 and μ x+ν y=0. α,β,μ and ν are i.i.d random variable. Each of them takes value 1 and 0 with equal…
Q45f(x,y)=x+y+xy where x,y∈ℜ₊₊. For c∈ℜ₊₊, let us define, L={(x,y)∈ℜ²| f(x,y)≤ c}, U={(x,y)∈ℜ²| f(x,y)≥ c}, I={(x,y)∈ℜ²| f(x,y)=c}. Which of the above…
Q46What is the total number of local maxima and local minima of the following function f(x)={ (2+x)³ if -3<x≤ -1; x^(2/3) if -1<x<2 }
Q47Suppose that f(x) is twice differentiable and strictly concave in x. Define, g(x)=lim_(t→ x)(f(c+t)-f(c+x))/(t-x) where c is a constant. Then g(x) is
Q48A rectangle has its lower left hand corner at the origin and its upper right hand corner on the graph of f(x)=x²+(1/x²). For which x is the area of…
Q49The real valued function f(x)=x+|x|+(x-1)+|x-1|, where |x|,|x-1| stand for absolute values
Q50Let x=(x₁,x₂,…,xₙ) and y=(y₁,y₂,…,yₙ) be two vectors in ℜⁿ. Define, x⊗ y=Σᵢ₌₁ⁿxᵢ|yᵢ|, where |yᵢ| stands for absolute value. How many of the…
Q51Consider an economy where the nominal wage rate is set by wage bargaining before production. The nominal wage Wₜ=Pₜ^eF(uₜ,Aₜ) with Fᵤ<0,F_A>0…
Q52Suppose the average productivity of workers remains constant at a level A̅. Given the relationship in previous question, which of the following…
Q53A one-shot increase in the average productivity of worker, ceteris paribus, leads to
Q54A one-shot increase in the producer's mark up, ceteris paribus, leads to
Q55Go back to the relationship between πₜ and πₜ^e above (first question of this list). Suppose expectations are static, i.e., πₜ^e=πₜ₋₁. Also let…
Q56Now suppose the workers productivity increases at a constant rate γ, that is, (Aₜ-Aₜ₋₁)/Aₜ₋₁=γ. To maintain a non-accelerating inflation rate, rate…
Q57Consider a small open economy with fixed nominal exchange rate E, fixed domestic price P and fixed foreign price P*, real exchange rate ε. The IS…
Q58Write the goods market clearing level of output as a function of the real exchange rate ε and other parameters. If you plot this relationship…
Q59Let us now bring in an asset market and a foreign exchange market. The asset market equilibrium (LM) is M̅=l₁Y-l₂r. The foreign exchange market…
Q60Let the equilibrium output and the equilibrium exchange rate be simultaneously determined by the intersection of the above two schedules (from the…