Re: Micro

Posted by arpita lahiri on
URL: http://discussion-forum.276.s1.nabble.com/Micro-tp5202707p5208817.html

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