Re: Micro

Posted by arpita lahiri on
URL: http://discussion-forum.276.s1.nabble.com/Micro-tp5202707p5208833.html

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
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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  
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a) u1 + u2 = (4 3 )(15)  
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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?
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a) (u1,  u2) = ((4 3 )(15)/2, (4 3 )(15)/2)  
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b) (u1,  u2) =((3 4 )(15)/2, (3 4 )(15)/2)  
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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