Top Posters
Since Sunday
25
13
11
9
5
l
4
4
R
4
M
4
k
4
w
3
M
3
New Topic  
corie corie
wrote...
Posts: 767
4 years ago
Natasha derives utility from attending rock concerts (r) and from drinking colas (c) as follows:
   U(c,r) = c.9r.1       
The marginal utility of cola (MUc) and the marginal utility of rock concerts (MUr) are given as follows:
   MUc = .9c-.1r.1      MUr = .1c.9r-.9 

a.   If the price of cola (Pc) is $1 and the price of concert tickets (Pr) is $30 and Natasha's income is $300, how many colas and tickets should Natasha buy to maximize utility?
b.   Suppose that the promoters of rock concerts require each fan to buy 4 tickets or none at all. Under this constraint and given the prices and income in (a), how many colas and tickets should Natasha buy to maximize utility?
c.   Is Natasha better off under the conditions in (a) or (b)?  Explain your answer.
Textbook 

Microeconomics


Edition: 8th
Author:
Read 529 times
10 Replies
Replies
Answer verified by a subject expert
boransalboransal
wrote...
Posts: 474
4 years ago
Sign in or Sign up in seconds to unlock everything for free
More questions for this book are available here
a.    
To maximize utility, Natasha (1) must be on her budget line, and (2) the marginal rate of substitution must equal the ratio of the prices of the goods.  The marginal rate of substitution is equal to the ratio of the marginal utilities of the goods.  Thus:
   (1)   c + 30r = 300       
   (2)   MUc/MUr = (.9c-.1r.1)/(.1c.9r-.9) = Pc/Pr = 1/30       
   Solving these equations simultaneously for c and r yields c = 270 and r = 1.

b.    
Without the 4 ticket constraint, Natasha would prefer to buy just 1 ticket.  If required to buy 4 tickets, Natasha would maximize utility by either buying 4 tickets and consuming 180 colas, or by buying zero tickets and consuming 300 colas.  The utility function may be used to determine which is preferred.  In this case, Natasha will buy zero tickets and 300 colas.    

c.    
Natasha prefers (a) because constraining the choice set never leaves one better off.  At best it has no effect.  Otherwise, the addition of a constraint leaves one worse off.
This verified answer contains over 210 words.

Related Topics

wrote...
A year ago
Hello, works great
wrote...
A year ago
goooooo
wrote...
A year ago
thank you
wrote...
A year ago
Thank you
wrote...
A year ago
Thak you
wrote...
11 months ago
wow
wrote...
5 months ago
Thank you so much
Post Merge: 5 months ago

thank you
wrote...
5 months ago
TY Slight Smile
Post Merge: 5 months ago

Thank you
wrote...
A month ago
Thanks!
New Topic      
Explore
Post your homework questions and get free online help from our incredible volunteers
  244 People Browsing
 498 Signed Up Today
Your Opinion
What's your favorite coffee beverage?
Votes: 205

Related Images
 719
 504
 401