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Delhi School of Economics MA Economics past year
papers (2006-2020)
Econschool
Contents
1 DSE 2006 2
2 DSE 2007 15
3 DSE 2008 30
4 DSE 2009 46
5 DSE 2010 60
6 DSE 2011 74
7 DSE 2012 88
8 DSE 2013 103
9 DSE 2014 116
10 DSE 2015 132
11 DSE 2016 147
12 DSE 2017 157
13 DSE 2018 168
14 DSE 2019 181
15 DSE 2020 192
1 DSE 2006
- Suppose A and B have to divide a box of chocolates and both of them prefer to have more chocolates to fewer chocolates. An allocation that gives all the chocolates to A is A. Pareto inefficient B. Pareto efficient C. Pareto unfair D. Pareto fair
- Among the effects of urban rent control are A. a disincentive to build for rental purposes B. an implicit redistribution of wealth from those who do not have rent-controlled housing to those who do have rent-controlled housing C. a low degree of mobility in housing market D. all of the above
- Processed and piped water is A. a public good B. a private good C. a private bad D. a public bad
- A situation in which all electricity generators in a state can sell their output only to the State Electricity Board is described as A. a monopoly B. a monopsony C. an oligopolistic market D. a monopolistically competitive market
- Consider a firm that produces single good using labor and capital. Let C, Q, L, K, w, r and p denote cost of production, output, labor input, capital input, the wage rate, the price of capital and the price of output respectively. An example of the cost function for the firm is A. C = wL + rK B. C = min{wL, rK} C. C = pQ/[wL + rK] D. C = Q√wr
- If the IS curve is downward sloping and the LM curve is vertical, a unit increase in government expenditure results in
A. Income elasticity of both goods x and y is 1. B. Income elasticity of good x is 0. C. Income elasticity of good y is 0. D. Income elasticity of good x is 1 and of good y is 0.
- Consider the experiment of tossing two unbiased coins in succession. What is the prob- ability of obtaining two heads, given that at least one of the coins comes up heads? A. 1/ 2 B. 1/ 4 C. 1/ 3 D. 2/ 3
- Suppose all input prices as well as output price double. The level of output produced by a profit-maximizing firm which uses a decreasing returns to scale technology will A. be double of its original level B. increase, but not necessarily double C. remain constant D. change, but we cannot say in which direction
- Consider an n × n matrix A with real entries. A is non-singular if and only if A. the determinant of A is not equal to 0 B. the columns vectors of A are linearly independent C. the row vectors of A are linearly independent D. any of the above three conditions is satisfied
- Consider a function f : R → R, where R denotes the set of real numbers. If f is increasing, i.e., x ≥ y implies f (x) ≥ f (y), then A. f is concave B. f is convex C. f is quasi-convex D. f is continuous
- Consider a singular n × n matrix A with real entries. Interchanging the positions of a pair of adjacent columns of A A. does not change the value of the determinant of A B. changes the sign of the determinant C. increases the value of the determinant D. decreases the value of the determinant
- There are three women on the platform of a train station. The train that they are waiting for has 5 coaches and each of them is equally likely to enter any coach. What is the probability that they will all enter the same coach? A. 12/ 25 B. 3/ 5 C. 3/ 125 D. 9/ 25 E. 1/ 25
- Suppose a neighborhood has 90 Hindus and 10 Muslims. What is the probability that two randomly selected persons from that neighborhood will have the same religion? A. 0. 5 B. 0. 81 C. 0. 9 D. 0. 82
- Exchange rate overshooting occurs A. under fixed exchange rates when the central bank mistakenly buys or sells too much foreign exchange B. under fixed exchange rates as a necessary part of the adjustment process for any monetary shock C. under flexible exchange rates when the exchange rate rises (depreciates) above and then falls down to equilibrium after a monetary expansion D. under flexible exchange rates, so that large financial shocks in the domestic economy have very little impact on exchange rates
- In an open economy with a system of fixed exchange rates A. monetary policy is an effective tool for stabilizing the economy B. fiscal policy is a by-product of exchange rate policy C. fiscal policy is an effective tool for stabilizing the economy D. both (a) and (b) above Answer 21, 22 and 23 for the following situation. Consider a competitive exchange economy with two agents (1 and 2) and two goods (X and Y ). Agent 1’s endowment of (X, Y ) is (0, 5) and Agent 2’s endowment of (X, Y ) is (10, 0). An allocation for Agent i is denoted (xi, yi), where xi is his allocation of X and yi is his allocation of Y. Agent i’s objective is to choose (xi, yi) to maximise his utility min{xi, yi}
- The allocation with (x 1 , y 1 ) = (3, 3) and (x 2 , y 2 ) = (7, 2) is A. a competitive equilibrium allocation and is Pareto efficient
D. equilibrium output does not change
- The aggregate production function in an economy at any time period t is given by Yt = min{Kt/ 2 , Lt/ 4 }, where Kt and Lt are respectively the aggregate stock of capital and the available stock of labour at time t. In each period, 20% of the total output is saved and invested, which augments the next period’s capital stock. Capital does not depreciate. Available labour stock grows by 4 units in every period. The economy currently has 200 units of capital and 420 units of labour. What is the current level of employment and what will be the level of employment tomorrow? A. Current Employment: 420; Employment tomorrow: 424 B. Current Employment: 400; Employment tomorrow: 424 C. Current Employment: 400; Employment tomorrow: 400 D. Current Employment: 420; Employment tomorrow: 420
- Members of the Gymkhana Club are charged quarterly fees on the basis of their average weight, rounded to the nearest kg. Of the 560 members, 120 weighed between 60 and 69 kg, 140 weighed between 70 and 79 kg, 170 weighed between 80 and 89 kg, and the remaining weighed between 90 and 99 kg. If members are charged Rs. 50 per kilo of their weight, on average how much must each member pay? A. Rs. 3800 B. Rs. 3900 C. Rs. 4000 D. Rs. 4100
- ICICI Bank collects data on 10000 respondents. Out of the 6800 men, 4200 have credit cards, and out of the 3200 women, 2500 have credit cards. Out of the men with credit cards, 1200 have unpaid balances, whereas out of the women with credit cards, 1400 have unpaid balances. What is the probability that an individual selected at random is a man without an unpaid balance? A. 0. 68 B. 0. 56 C. 0. 12 D. 0. 84
- A monopolist has two plants. In plant 1, the total cost function is c 1 (q 1 ) = 2q 1 and in plant 2, the total cost function is c 2 (q 2 ) = q 22 /2, where q represents the quantity of good produced. The demand faced by the monopolist is p = 10 − q, where q = q 1 + q 2. How does the monopolist allocate its total production to serve the market? A. q 1 = 6 and q 2 = 2 B. q 1 = 2 and q 2 = 2 C. q 1 = 4 and q 2 = 4
D. q 1 = 4 and q 2 = 10/ 3
- There are two individuals A and B. The utility function of both individuals are identical and given by u(x, y) = max{x, y}. Each of them has 1 unit of good x and 1 unit of good y. Which of the following is a Pareto optimal allocation? A. A has x = 1, y = 1 and B has x = 1, y = 1 B. A has x = 2, y = 0 and B has x = 0, y = 2 C. A has x = 0, y = 0 and B has x = 2, y = 2 D. A has x = 3/ 2 , y = 1/2 and B has x = 1/ 2 , y = 3/ 2 Answer 31, 32 and 33 for the following information. Three players A, B and C take turns playing a game as follows. A and B play in the first round. The winner plays C in the second round, while the loser sits out. The winner of the second round plays the person who was sitting out. The game continues in this fashion, with the winner of the current round playing the next round with the person who sits out in the current round. The game ends when a player wins twice in succession; this player is declared the winner of the contest. For any of the rounds, assume that the two players playing the round each have a probability 1/2 of winning the round, regardless of how the past rounds were won or lost.
- The probability that A becomes the winner of the contest is A. 5/ 14 B. 1/ 2 C. 3/ 7 D. 7/ 16
- The probability that C becomes the winner of the contest is A. 1/ 7 B. 1/ 5 C. 1/ 8 D. 2/ 7
- The probability that the game continues indefinitely, with no one winning twice in suc- cession, is A. 1/ 1023 B. 0 C. 1/ 223 D. 1/ 216
- Consider collecting a random sample that has two observations, from a population that is normally distributed with mean μ and variance 16. The variance associated with the distribution of twice the difference between these two observations equals
B. the amounts of inputs used C. the number of firms in the industry D. the level of profits Answer 40 and 41 for the following situation. Consider a market served by a pair of firms, 1 and 2. The inverse market demand is given by p = 1 − (x 1 + x 2 ), where xi is the output of Firm i. Let Firm 1’s cost function be C 1 (x 1 ) = x 1 /2 and Firm 2’s cost function be C 2 (x 2 ) = x 2 / 3
- If Firms 1 and 2 are Cournot duopolists, then Cournot equilibrium outputs are A. (x 1 , x 2 ) = (4/ 18 , 4 /18) B. (x 1 , x 2 ) = (2/ 18 , 5 /18) C. (x 1 , x 2 ) = (5/ 18 , 3 /18) D. (x 1 , x 2 ) = (0, 1 /3)
- Now suppose the situation changes so that Firm 1 chooses x 1 first and Firm 2 chooses x 2 after observing Firm 1’s choice. Relative to Cournot situation, in this new situation, A. x 1 and x 2 decrease B. x 1 decreases and x 2 increases C. x 1 increases and x 2 decreases D. x 1 and x 2 increase
- Suppose Asha’s preferences between two commodities x 1 and x 2 can be represented by u(x 1 , x 2 ) = min{x 1 − 5 , x 2 + 3}. Given an income of Rs. 73, and facing prices of Rs. 3 for x 1 and Rs. 4 for x 2 , Asha’s optimal consumption bundle of (x 1 , x 2 ) will be A. (12. 5 , 4 .5) B. (10. 42 , 10 .42) C. (15, 7) D. (3, 16)
- Consider the following macroeconomic model:
C = 2000 + 0. 4 YD I = 500 − 10 r + 0. 4 Y G = 400 T = 1000 (M/P )D^ = 0. 2 Y − 50 r (M/P )S^ = 1000 where YD is disposable income. The equation of the IS curve for this model is A. Y = 9500 − 50 r
B. Y = 12500 − 50 r C. Y = 14500 − 100 r D. Y = 14500 − 60 r
- A negative supply shock (e.g., oil price increase) shifts the Phillips curve and the natural rate of unemployment. If the government wants to keep the economy at the original rate of unemployment, it must have inflation. A. lowers, ever increasing B. raises, ever decreasing C. raises, ever increasing D. does not change, ever increasing
- An increase in foreign income the equilibrium output of a small open economy with uncovered interest parity and flexible exchange rates. A. increases B. decreases C. leaves unchanged D. first increases then decreases
- Amit has a box containing 6 red balls and 3 yellow balls. Amita has a box containing 4 red balls and 5 yellow balls. Amit randomly draws one ball from his box and puts it into Amita’s box. Now Amita randomly draws one ball out of her box. What is the probability that balls drawn by Amit and Amita were of different colours? A. 1/ 3 B. 2/ 15 C. 4/ 15 D. 7/ 15
- Two patients share a hospital room for two days. Suppose that, on any given day, a person independently picks up an airborne infection with probability 1/4. An individual who is infected on the first day will certainly pass it to the other patient on the second day. Once contracted, the infection stays for at least two days. What is the probability that both patients have contracted the infection by the end of the second day? A. 125/ 256 B. 121/ 256 C. 135/ 256 D. 131/ 256
- Consider a function f : R → R, where R, where R denotes the set of real numbers. If f is strictly increasing (i.e., x > y implies f (x) > f (y)) and differentiable, then the derivative of f A. may be less than 0 at some x ∈ R B. may be infinite at some x ∈ R C. is greater than or equal to 0 at every x ∈ R D. is greater than 0 at every x ∈ R
- Consider the following claim: ”There is some general election and some party such that all the candidates of that party in that election are honest.” If this claim is false, then which of the following statements must be true? A. In every election, there exists a party such that all its candidates are dishonest. B. There is some general election and some party such that all the candidates of that party in that election are honest. C. In every election, all candidates of all parties are dishonest. D. In every election, every party has at least one dishonest candidate. Answer 54, 55, 56 and 57 using the following information. Consider a society consists of individuals who may belong to various sets called Family and/or Gangs. The collections of Families and Gangs satisfy the following rules:
- The entire society is a Family.
- The empty subset of a Society is also a family.
- Given a collection of Families, the set of individuals who belong to every Family in that collection is also a Family.
- Given any two Families, the set of individuals who belong to either of the two Families is also a Family.
- A set of individuals is called a Gang if and only if the set of individuals not in it constitute a Family.
- The intersection of two Gangs is necessarily A. a Family B. a Gang C. not a Family D. not a Gang
- The union of a collection of Gangs is necessarily A. not a Family B. not a Gang C. a Family
D. a Gang
- Which of the following statements is necessarily true? A. A set of individuals cannot be a Gang and a Family. B. There are at least two sets of individuals that are both a Family and a Gang. C. The union of a Family and a Gang is a Gang. D. The intersection of a Family and a Gang is a Family.
- Suppose we are given a Family and a Gang. Then, the set of individuals who belong to the given Family but not to the given Gang necessarily constitute A. a Family B. a Gang C. neither a Family, nor a Gang D. a Family and a Gang
- You have 10 pockets. What is the smallest number of one rupee coins you need to have a different number of coins in each pocket? A. 45 B. 35 C. 60 D. 50
- There are 3 red and 5 black balls in an urn. You draw two balls in succession without replacing the first ball. What is the probability that the second ball you draw is red? A. 2/ 7 B. 3/ 8 C. 5/ 7 D. 1/ 4
- Given that R denotes the set of real numbers, which of the following mappings is a one-to-one (i.e., injective) function? A. f (x) = tan x, where x ∈ R and x ≥ 0 B. f (x) = |x|, where x ∈ R C. f (x) = 1/x, where x ∈ R and x ≥ 0 D. f (x) = |x|, where x ∈ R and x ≥ 0
F ood(F )
Clothing(C)
O 30 40
Original Budget Line
C
B
D
A
A. A, B
B. A, D
C. B, C
D. C, D
- NAIRU implies A. the unemployment rate is zero B. inflation is contant C. the rate of growth of real GDP is constant D. none of the above
- In an open economy with perfect capital mobility and fixed exchange rates, an open market operation will A. increase output and reduce interest rate B. increase the money supply C. lower the trade deficit D. change the composition of the monetary base
- If a person is a borrower, a rise in the interest rate will A. always reduce borrowing B. always increase borrowing C. could increase borrowing depending on the relative strengths of income and substitution effects D. none of the above
- The J-curve suggests that the effect of an appreciation of the exchange rate on the trade balance is to:
A. improve it in the short run B. worsen it in the short run C. leave it unchanged D. improve it in the long run
- Under classical supply conditions, a fiscal expansion A. only raises the price level and the interest rate B. expands supply at constant prices C. expands supply at rising prices D. leaves both supply and price level unchanged
- Consider the following functions f : R → R, where R denotes the set of real numbers. Which of the following functions is quasi-convex? A. f (x) = x^2 B. f (x) = cos x C. f (x) = e−x D. f (x) = x−^1 if x 6 = 0; f (x) = 0 if x = 0
- Consider 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 A. det A < det B B. det A > det B C. det A = det B D. the sign of det A is the opposite of the sign of det B
- Consider a strictly decreasing (i.e., x > y implies f (x) < f (y)) and differentiable function f : R → R, where R denotes the set of real numbers. Denote the derivative of f at x ∈ R by Df (x). Which of the following may be true about f? A. Df (x) > 0 for some x ∈ R B. Df (x) = 0 for some x ∈ R C. Df (x) = 0 for every x ∈ (a, b) where a < b D. Df (x) ≥ 0 for every x ∈ R
- If 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 statements must be true? A. In every legislature and every party, all legislators do not pay taxes B. There exists a legislature such that every legislator in every party does not pay taxes
A. (i) 0.16; (ii) 0. B. (i) 0.16; (ii) 0. C. (i) 0.24; (ii) 0. D. none of the above
- Let Y denote the number of heads obtained when 3 coins are tossed. The variance of Y 2 is A. 6. B. 7. C. 7. D. 8.
- A firm has the production function Q = 12L − L^2 , where L is labour input and Q is output. If the firm is a monopolist with a demand curve P (Q) = 100 − Q, what is the MRPL (Marginal Revenue Product of Labour) curve? A. 1200 − 288 L + 72L^2 − 4 L^3 B. 1200 − 288 L − 72 L^2 + 4L^3 C. 1200 − 488 L + 72L^2 − 4 L^3 D. 1200 − 488 L − 72 L^2 + 4L^3
- Sudhir lives in Gujarat. His total wealth next year, including his house, will be Rs. 5,00,000. There is a 10% chance that a big earthquake will occur next year and com- pletely destroy his house, valued at Rs. 2,00,000. (i) What is Sudhir’s expected wealth next year if he chooses not to buy house insurance? (ii) Suppose Sudhir’s utility function is given by U (W ) = W 0.^5 , where W repre- sents total wealth in thousands of rupees. Is Sudhir risk-averse, risk-loving, or risk-neutral? A. (i) Rs. 4,50,000 and (ii) risk-averse B. (i) Rs. 4,50,000 and (ii) risk-neutral C. (i) Rs. 4,80,000 and (ii) risk-loving D. (i) Rs. 4,80,000 and (ii) risk-averse
- Consider an airport that produces noise (N ) that declines as the distance (d) in kilome- tres, from the airport increases: N (d) = 1/(d^2 ). Praful works at the airport. Praful’s damage from noise is Rupee 1 per unit of noise and is associated with where Praful lives. His costs of commuting are Rupee 1 per kilometre (each way). The closest he can live to the airport is d = 0.1 km. (i) What is the distance Praful will live from the airport in the absence of com- pensation for the noise?
(ii) Suppose Praful is compensated for his damage, wherever he may live. How much will he be compensated? A. (i) 1 km and (ii) Rs. 100 B. (i) 0.1 km and (ii) Rs. 100 C. (i) 1 km and (ii) Rs. 1 D. (i) 0.1 km and (ii) Rs. 100
- Suppose the car market is perfectly competitive and each firm has the same cost struc- ture. There are 1000 firms in the industry. The market demand and cost schedules are given below.
Market Demand Price (lacs per car) 3.65 5.20 6.80 8.40 10.00 11.60 13. Quantity (thousands per year) 500 450 400 350 300 250 200 Costs per firm (Rs. lacs) Output 200 250 300 350 400 450 500 MC 6.40 7.00 7.65 8.40 10.00 12.40 12. AVC 7.80 7.00 7.10 7.20 7.50 8.00 9. ATC 12.80 11.00 10.43 10.06 10.00 10.22 11.
In the long run A. Some firms will exit the industry, but others will remain B. Some firms will enter the industry C. The number of firms will remain the same D. The industry will close down
- Abhik’s and Brinda’s demand curves for apples are given by
p = 20 − q (Abhik) p = 5 − (q/2) (Brinda) where p, q ≥ 0 for each. Suppose these are the only two consumers in the market, and the market supply function is given by: p = 2 + Q. Then the equilibrium quantity in the market is: A. 12 apples B. 9 apples C. 6 apples D. 3 apples
