DSE 2007 question paper

All 57 questions from the DSE 2007 Delhi School of Economics MA entrance paper. Open any question for the worked solution.

Q1Consider a consumer having a utility function U=2x+y where x and y are two commodities. Suppose the price of x and y are both Rs. 5 each and the…
Q2With quantity of x on the horizontal axis, the Engel curve for commodity x corresponding to the utility function U=y+f(x) will be
Q3Suppose a producer has a fixed coefficient technology Q=min (2K,3L), where Q is output and K and L are the inputs. At equilibrium
Q4A monopolist will never produce a quantity where the price elasticity of demand is inelastic because:
Q5In the figure, the original budget line was 5F+10C=200, and Anita purchased 30 units of F and 5 units of C. At two later dates, budget lines (1) and… · diagram
Q6NAIRU implies
Q7In an open economy with perfect capital mobility and fixed exchange rates, an open market operation will
Q8If a person is a borrower, a rise in the interest rate will
Q9The J-curve suggests that the effect of an appreciation of the exchange rate on the trade balance is to:
Q10Under classical supply conditions, a fiscal expansion
Q11Consider functions f:ℜ→ℜ. Which of the following functions is quasi-convex?
Q12Consider an n× n matrix A with real entries. If matrix B is derived by adding the first column of A to the last column of A, then
Q13Consider a strictly decreasing (i.e., x>y implies f(x)<f(y)) and differentiable function f:ℜ→ℜ, with derivative Df(x). Which of the following may be…
Q14If the statement 'There exists a legislature and a party such that every legislator in that party pays taxes' is false, then which of the following…
Q15If f:ℜⁿ→ℜ is twice differentiable, concave and homogeneous of degree 1, then the Hessian matrix of f is
Q16Five fibers of lengths 1, 2, 3, 4 and 5 inches are tested to see which breaks first. The probability that any fiber breaks first is proportional to…
Q17Which of the following statements is WRONG? A probability density function f(x)
Q18A primary school has 6 classes, numbered from 1 to 6. Class 1 has twice as many students as each of the other classes. What is the probability that…
Q19A traffic light on the way to the University is red 40% of the time. What is the probability of getting a red light (i) 2 days in a row; (ii) any 2…
Q20Let Y denote the number of heads obtained when 3 coins are tossed. The variance of Y² is:
Q21A firm has the production function Q=12L-L², where L is labour input and Q is output. If the firm is a monopolist with a demand curve P(Q)=100-Q…
Q22Sudhir's total wealth next year, including his house, will be Rs. 5,00,000. There is a 10 percent chance a big earthquake occurs next year and…
Q23An airport produces noise N that declines with distance d (km): N(d)=1/d². Praful works at the airport; his damage from noise is Rupee 1 per unit of…
Q24The car market is perfectly competitive with 1000 identical firms. Market demand: at prices (Rs lacs) 3.65, 5.20, 6.80, 8.40, 10.00, 11.60, 13.20…
Q25Abhik's and Brinda's demand curves for apples are p=20-q (Abhik) and p=5-(q/2) (Brinda), with p,q≥ 0. They are the only two consumers, and market…
Q26A farmer's demand for wheat is q=25+m/(20p), where m is money income and p is the price. Money income is Rs. 1000. Initially the farmer buys wheat…
Q27An economy has agents 1 and 2 and 3 units each of goods X and Y. An allocation is ((x₀,y₀),(x₁,y₁),(x₂,y₂)) with (x₀,y₀) left over. Each agent faces…
Q28Let a=1 for Agent 2's utility function. Then, the equilibrium allocation in the above question is
Q30Now suppose Agent 2 is higher on the social ladder, so Agent 2 chooses first; a=2. Which allocation ((x₀,y₀),(x₁,y₁),(x₂,y₂)) is an equilibrium for…
Q32(Same wage-price economy.) There will always be full employment of the aggregate stock of labour force if and only if the expected and the actual…
Q33With a technology where one employed worker produces one unit of output (so Y=N, and u=1-Y/L̅), an increase in output ceteris paribus leads to
Q34(Same setup.) An increase in the aggregate stock of labour force ceteris paribus leads to
Q35Consider the macro model: C=α₀+α₁Y, I=β₀+β₁Y-β₂i, G=G̅, with α₁+β₁<1; money market M̅/P=γ₁Y-γ₂i. If the interest rate i increases by one unit, to…
Q36(Same model.) A unit increase in government expenditure (G) will increase the equilibrium income level (Y) by
Q37Savitri works for 2 months with wages w₁ and w₂, planning consumption c₁,c₂ to maximize log c₁+1/(1+δ)log c₂, δ>0. She may borrow from her employer…
Q38Assuming that the above condition is satisfied, when the discount rate (δ) goes up, her borrowing
Q39Two open economies with fixed exchange rates (rate = unity), i=1,2: Cᵢ=c₀ᵢ+c₁ᵢ(Yᵢ-Tᵢ), Iᵢ=I̅ᵢ, Gᵢ=G̅ᵢ, Tᵢ=tᵢYᵢ, imports Mᵢ=m₀ᵢ+m₁ᵢYᵢ (each country's…
Q40In the Mundell-Fleming model of a small open economy with flexible exchange rates and perfect capital mobility, starting from equilibrium, if…
Q41f:ℜⁿ→ℜ is convex if and only if
Q42If f:ℜ₊→ℜ is defined by f(x)=∫ₓ^(x²)e^t dt, then the derivative of f at x>0 is
Q43The sequence (xₙ), where xₙ=(-1)ⁿ(1+n⁻¹) and n=1,2,…
Q44The set ⋂ₙ₌₁^∞(-1-n⁻¹, 1+n⁻¹) is identical to
Q45The set ⋃ₙ₌₁^∞[-1+n⁻¹, 1-n⁻¹] is identical to
Q46For x,y∈ℜⁿ, let d(x,y)=max {|xᵢ-yᵢ | i=1,…,n}. Which of the following relations holds for all x,y,z∈ℜⁿ?
Q47Given sets X, Y, let X× Y={(x,y)| x∈ X and y∈ Y} and X-Y={x∈ X| x∉ Y}. Which of the following formulae is generally correct for sets A, B and C?
Q48Suppose f:ℜ²→ℜ is defined by z=xy. At (0,0) this function
Q49What is the maximum value of the function z=xy subject to the constraints x>0, y>0, and 2x+y=6?
Q50'Beautiful cities repel people. Look at India's most beautiful cities: they are among the least populated cities of the country.' Which of the…
Q51The average travel time to a distant city is w hours by train or z hours by bus. A man cannot decide whether to take the train or the bus, so he…
Q53Suppose that each person out of a group of 4 friends is randomly assigned to one of 6 classes. What is the probability that no class has more than…
Q54A continuous random variable has the probability density function f(x)=1/3 for x between -1 and +2, and 0 elsewhere. Its mean, variance and median…
Q55The joint probability distribution of A (age in years) and W (weight one can lift) is given. The marginal probabilities of A are: P(15)=0.06…
Q56In a survey of 400 likely voters, 215 responded that they would vote for the ruling party. Let p be the fraction of all likely voters preferring the…
Q57Let X and Y be two random variables with E[X]=3, E[Y]=0, V[X]=4, V[Y]=25, and E[XY]=5. Find (i) Cov[X,Y]; (ii) the Pearson correlation coefficient…
Q58If Y is a binomial random variable with parameters n=4 and p=0.78, calculate Pr (Y≥ 3) to 2 decimal places.
Q59An examination was given to two classes of 40 and 50 students. In the first class the mean grade was 74 with standard deviation 8; in the second…
Q60A sample poll of 300 voters from District A and 200 from District B showed 56% and 48% respectively in favour of a candidate. At a 5% level of…