Micro
Locked
 
|
How to find demand in this
Q:Consider a person who consumes water and fruits, deriving utility min{2x + 5y, 5x + 2y) if x is the amount of water consumed and y is the amount of fruit consumed. Suppose this person’s income is Rs. 12,the unit price of fruit is Rs. 4 and the unit price of water facing this person is Re. 1. The price of water incorporates a per unit of subsidy of Re. 1, i.e., for every unit of water consumed by this person, she pays Re. 1 to the water supplier and the government pays Re. 1 to the water supplier. Suppose this person’s demand is (x0, y0). 1. Suppose the water subsidy is removed and she has to pay Rs. 2 for each unit of water. Let (x1, y1) be the new demand. What is the resulting change in this person’s demand, i.e., what is (x1 – x0, y1– y0) a) (-10, 2) b) (-6, 0) c) (-0.4, -0.4) d) (3.6, -2.4) |
|
|
How to go threw this question
Q2:. Let X stand for the consumption set and let R, I, P respectively stand for the weak preference relation, indifference relation and strict preference relation of a consumer. The weak preference relation R is said to satisfy Quasitransitivity if and only if for all x, y, z belonging to X, xPy and yPz → xPz. Which of the following preference relations over X = {x,y,z} satisfy Quasitransitivity? a) xPy & yPz & zPx b) xPy & yPz & zIx c) xPy & yIz & zIx d) yPx & yIz & xPz |
|
|
it is option(c) u go by ruling out, all the other options donot satisfy the property, and this option is trivially true, bcoz v cannot check the preference relation here
On Mon, Jun 21, 2010 at 7:46 AM, NIDHI [via Discussion forum] <[hidden email]> wrote: How to go threw this question |
|
|
In reply to this post by nidhi aggarwal
Q:Consider a person who consumes water and fruits, deriving utility min{2x + 5y, 5x + 2y) if x is the amount of water consumed and y is the amount of fruit consumed. Suppose this person’s income is Rs. 12,the unit price of fruit is Rs. 4 and the unit price of water facing this person is Re. 1. The price of water incorporates a per unit of subsidy of Re. 1, i.e., for every unit of water consumed by this person, she pays Re. 1 to the water supplier and the government pays Re. 1 to the water supplier. Suppose this person’s demand is (x0, y0). 1. Suppose the water subsidy is removed and she has to pay Rs. 2 for each unit of water. Let (x1, y1) be the new demand. What is the resulting change in this person’s demand, i.e., what is (x1 – x0, y1– y0)
a) (-10, 2) b) (-6, 0) c) (-0.4, -0.4) d) (3.6, -2.4) how to find the demand schedule plz help me |
|
|
The outcome of an experiment are represented by the points in the square bounded by x =
0, y = 0, x = 1, y = 1 in XY-plane. If probability is distributed uniformly, what is the 2 2 probability that x + y > 1? a) (4 – p)/4 b) p/4 c) 0 d) None of the above. how 2 get the ans plz tell d process |
|
|
2. Consumer A’s preferences are represented by the following utility function
uA(x, y) = x + y, if x + y = 2 = x + y +2, otherwise Consumer B’s preferences are represented by the following utility function uB(x, y) = x, if x = y = y, otherwise a) Consumer A’s preference is continuous and Consumer B’s preference is not continuous. b) Consumer A’s preference is not continuous and Consumer B’s preference is continuous. c) Both consumers’ preferences are continuous. d) Both consumers’ preferences are not continuous. 3. We define the sequence of functions fn on the interval [0, 1] by 2 fn(x) = n x if x ? [0, 1/n] 2 = 2n – n x if x ? [1/n, 2/n] = 0 otherwise a) For every x, the sequence of numbers (fn(x)) has a limit in the space of real numbers. b) limn?8 fn(x) does not exist for any x. c) When limn?8 fn(x) exists, the actual limit depends upon on the x in question. d) limn?8 fn(x) exists for all but finitely many x. 4. Continuing with the sequence of functions above, we consider the sequence of real numbers ( ?fn ) (that is the sequence of their integrals). This sequence of integrals is a) An increasing sequence b) A decreasing sequence c) A constant sequence d) An oscillating sequence how 2 get the ans |
|
|
(Problems 1-3 are based on the following information) Consider a two-person (A and
B) two good (x and y) competitive exchange economy with externalities. A has utility function uA = 2(min{xA, yA}) - xB B has utility function uB = 4xB +4yB Both have the nonnegative quadrant as a consumption possibility set. A’s initial endowment is 12 units of x and 12 units of y; and B’s initial endowment is 12 units of x and no y. 1. Consider the following allocations: i) ((xA, yA),(xB, yB)) = ((24, 0), (0, 12)) ii) ((xA, yA),(xB, yB)) = ((12, 12), (12, 0)) Which of the following is true about the allocations above? a) Only i) is pareto efficient b) Only ii) is pareto efficient c) Both i) and ii) are pareto efficient d) None of the above 2. Example(s) of competitive equilibrium allocation is(are) a) ((xA, yA),(xB, yB)) = ((24, 0), (0, 12)) b) ((xA, yA),(xB, yB)) = ((12, 12), (12, 0)) c) ((xA, yA),(xB, yB)) = ((24, 12), (0, 0)) d) All of the above 3. An example of competitive equilibrium price is a) (4/9, 5/9) b) (5/9, 4/9) c) (1, 0) d) (0, 1) *Additional exercise(not part of the quiz): Determine the set of all pareto efficient allocations and competitive equilibria. 4. Let X be distributed uniformly on the interval [-1, 1] i.e. Probability distribution function of X is given by F(x) = (x+1)/2 for -1 = x = 1 Probability distribution function of Y = |X| is given by a) G(y) = y for 0 = y = 1 b) G(y) = 1 for 0 = y = 1 2 c) G(y) = y for 0 = y = 1 d) None of the above. 5. There is a pile of 18 matchsticks on a table. Players 1 and 2 take turns in removing matchsticks from the pile, starting with player 1. On each turn, a player has to remove a number of sticks that equals either 1or 2, such that the number of matchsticks that remain on the table equals some non-negative integer. The player, who cannot do so, when it is his /her turn, loses. Which of the following statements true? a) If player 2 plays appropriately, he/she can win regardless of how 1 actually plays. b) If player 1 plays appropriately, he/she can win regardless of how 2 actually plays. c) Both players have a chance to win, if they play correctly. d) The outcome of the game cannot be predicted on the basis of the data given. An n × n chessboard is coloured in the following way: the (i, j) square (that is, the square on the ith row and jth column) is coloured white if (i + j) is ev and black if (i + j) is odd. A coin placed on the (i, j) square can be moved to 2 2 (i’, j’) square if (i – i’) + (j – j’) is an even number. i. if a coin can be moved from one square to another, then the squares mus be of the same colour. ii. For n even, it is possible for a coin to travel from the square (1, 1) to th square (1, n) by a sequence of moves. Which of the following statements is true? a) Both i and ii are true. b) i is true and ii is false. c) i is false and ii is true. d) Both i and ii are false. how to get the ans |
|
|
1. Consider the following social choice problem in the setting of consumption of two goods by two
consumers. The two goods are called x and y and the two consumers are 1 and 2. Consumer 1 3/7 4/7 3/7 4/7 has utility function U1(x, y) = x y . Consumer 2 has utility function U2(x, y) = x y . The social endowment consists of 15 units of x and 20 units of y. Consumption contract curve is given by a) {((x1, y1),(x2, y2))| y1 = x1, x1 + x2 = 15 and y1 + y2 = 20} b) {((x1, y1),(x2, y2))| y1 = (4/3)x1, x1 + x2 = 15 and y1 + y2 = 20} c) {((x1, y1),(x2, y2))| y1 = (3/4)x1, x1 + x2 = 15 and y1 + y2 = 20} d) {((x1, y1),(x2, y2))| y1 = 2x1, x1 + x2 = 15 and y1 + y2 = 20} 2. Consider the situation of the preceding question, utility possibility frontier is given by 4/7 -4/7 a) u1 + u2 = (4 3 )(15) 4/7 -4/7 b) u1 + u2 = (3 4 )(15) c) u1 + u2 = 15 d) u1 + u2 = 35 3. Consider the situation of the preceding question, suppose that a social dictator has social welfare 1 2 functional of the following form: Social welfare as a function of (u , u ) is a weighted sum with 1 2 weight 2 on the lesser of u and u and weight 1 on the greater of the two. Which of the following functions can represent the preferences of the dictator? 1 2 2 1 a) Min{2u +u , u +2u } 1 2 2 1 b) Max{2u +u , u +2u } 1 2 c) u +u d) None of the above 4. Continuing with the previous question, what will be the welfare optimum plan chosen by this social planner? 4/7 -4/7 4/7 -4/7 a) (u1, u2) = ((4 3 )(15)/2, (4 3 )(15)/2) 4/7 -4/7 4/7 -4/7 b) (u1, u2) =((3 4 )(15)/2, (3 4 )(15)/2) 4/7 -4/7 c) (u1, u2) =(0, (4 3 )(15)) d) (u1, u2) =(7.5, 7.5) 5. A 4-sided die has its four faces labeled as a, b, c, d. Each time the die is rolled, the result is a, b, c, or d, with probabilities pa, pb, pc, pd, respectively. Different roles are statistically independent. The die is rolled 3 times. Let Na and Nb be the number of rolls that resulted in a or b, respectively. Find the covariance of Na and Nb. a) papb b) 3papb c) -1 d) None of the above 6. There are N individuals located in the interval [0.1]. The location of individual i is denoted by xi, where 0 = xi = 1. A social planner has to decide the location of a swimming pool in [0,1]. If the ? pool is built at y, where y [0,1], then individual i obtains utility -|y- xi|. Suppose the planner wishes to maximize the utility of the worst off individual by his choice of pool location. What location will he choose? a) Min{x1, x2, x3, ..xn} b) ?xi/n c) Median{x1, x2, x3, ..xn} d) (Min{x1, x2, x3, ..xn} + Max{x1, x2, x3, ..xn} )/2 how to get ans |
|
|
1. Consider a random variable X which can take only non zero integer values from -20 to +20, and
whose probability distribution is symmetric around 0. Suppose the function f(x), called the probability mass function of X, gives the probability that X = x, ? x = -20,…,-1, 1, ….,20. Now consider the random variable Y = max{X, -X}. Which of the following would be an appropriate definition for g(y), the probability mass function for Y? a) g(y) = max{f(y), f(-y)} ? y = 1, 2, …..,20 and g(y) = 0 otherwise. b) g(y) = 2f(y) ? y = 1, 2, …..,20 and g(y) = 0 otherwise. c) g(y) =f(max{y, -y}) ? y = 1, 2, …..,20 and g(y) = 0 otherwise. d) None of the above 2. Consider an exchange economy with persons 1 and 2 and goods x and y. Person 1’s utility x function is u1(x, y) = min{x, y} and u2(x, y) = e . The total endowment of the economy is (2,1). Which of the following is true about this economy? a) All feasible allocations are efficient b) Only allocations on the diagonal from 1’s origin to 2’s origin is efficient c) Only allocations on the four boundaries of the edgeworth box are efficient d) None of the above 3. Consider the situation of the preceding question. If person 1’s endowment is (1, 1) and 2’s endowment is (1, 0), then the following allocation is a competitive equilibrium a) (x1, y1) = (1, 1) (x2, y2) = (1, 0) b) (x1, y1) = (1, 0) (x2, y2) = (1, 1) c) (x1, y1) = (1.5, 0.5) (x2, y2) = (0.5, 0.5) d) None of the above 4. Consider the situation of the preceding question. Which of the following is(are) equilibrium price vectors? a) (px, py) = (8/13, 5/13) b) (px, py) = (1/2, 1/2) c) (px, py) = (1, 0) d) All of the above 5. Duopolists producing substitute goods q1 and q2 face inverse demand schedules: p1 = 18 + (½) p2 – q1 And p2 = 18 + (½) p1 – q2 respectively. Firm1 has marginal cost c and no fixed costs. Firm 2 has no costs. Each firm is a cournot competitor in price, not quantity. Compute the cournot equilibrium in this market, giving equilibrium price for each good. (Hint: Write the profit functions of two firms as a function of p1 and p2 and not quantities then compute the cournot equilibrium) a) (p1, p2) = (12+8c/15, 12+2c/15) b) (p1, p2) = (12+2c/15, 12+6c/15) c) (p1, p2) = (12, 12) d) None of the above 1 Definition 1: Relation between a set S and a set T is a subset of the Cartesian produc In particular, a relation on a set S is a subset of S X S. A binary relation R on the set S is formally defined as a subset of S X S – write R ? and (x, y) ? R if the ordered pair (x, y) is in relation R. Another way to write (x, y) ? Illustrations: Suppose S = {1, 2, 3}, given below are some examples of relations on S R1 = {{1,2), (2,2), (2,3)} R2 = {(1,1), (2,3)} R3 = = defined as (x, y) ? R3 iff x = y. Hence R3 = {(1,1), (1,2), (1,3), (2,2), (2,3), (3,3)} Definition 2: (a) Reflexivity: ? x ? S : (x, x) ? R (b) Completeness: ? x, y ? S : x ? y ? (x, y) ? R or (y, x) ? R (c) Transitivity: ? x, y, z ? S : ((x, y) ? R & (y, z) ? R) ? (x, z) ? R (d) Symmetry: ? x, y ? S : (x, y) ? R ? (y, x) ? R (e) Anti-symmetry: ? x, y ? S : ((x, y) ? R & (y, x) ? R) ? x = y (f) Asymmetry: ? x, y ? S: (x, y) ? R ? (y, x) ? R Consider the relation < on (strictly less than) where is the set of integers. WhicZ Z following is true? a) Relation < is reflexive and complete. b) Relation < is transitive, symmetric and complete. c) Relation < is transitive, complete, asymmetric and anti-symmetric. d) Relation < is transitive, symmetric and asymmetric. how 2 get the ans |
|
|
In reply to this post by nidhi aggarwal
Q1> its (-10, 2)
:)
|
|
|
In reply to this post by arpita lahiri
Hi! Arpita
ans to Q1 is only 2 is pareto efficient. bcoz there is no way of improving utility of one consumer without reducin others (i) is nt pareto efficient bcoz if allocation is (18 , 16) and (6,6) then the utility of individual 1 is 32-6 = 28 and utility of consumer 2 is 12*4 = 48(as earlier) |
|
|
In reply to this post by arpita lahiri
arpita
ans to q no 2 is (ii) |
«
Return to General Discussions
|
1 view|%1 views
| Free forum by Nabble | Edit this page |