New office hours: Fridays 3:30pm-5:30pm

 

Midterm statistics:

mean:49

max:70

 

 

Some Comments/Solutions for the Final:

Notice: The bluebook will not be returned until the end of the 4th Mini. If you want to have a look at it before that time, you can come to my office hour. 

 

Q1: Please follow the lecture notes. Notice that in Step 3 when you claim "lambda*px<px" if 0<lambda<1, you need to mention "px>0" first.

 

Q2: a. Here since there is a utility representation so the preferences are complete preorders. It is not necessarily to be continous.

b.No more assumptions are needed.  Some people add some assumptions to ensure the existence of the equilibrium. It's not necessary but I didn't take off points as long as it looks reasonable.

c.No equilibrium here.

d.The largest set is just the whole set...just define U1=10 and U2=20 for any allocation. Some people misunderstood the question. 

 

Q3:

a.Trivial

b.The two existence theorems definitely fail since Z might not be well defined now. 

   For the welfare theorems, the answer is ambiguous:

   If you follow the lecture notes(which require stronger assumptions), then both welfare theorems fail. 

   If you follow Mas-Colle's book, you can say they work. 

   Both answers are reasonable as long as you explain the reason briefly.

 

Q4.

a.Here I expect you to answer:

Z is continuous when price is strictly positive, homogenous degree 0 in p, Walras Law, bounded below. Notice that boundary condition does not necessarily hold.(Check Your Recitation Notes!)

 

b. In this case there is a representative agent(with Cobb-D preference and aggregate endowment), his/her excess demand is just the same as the original economy's excess demand. (Recall a homework question...). Few people got the right answer.

 

Q5. No unique solution. Any answer that looks reasonable is OK. I was not harsh on this question.