DEPARTMENT OF ECONOMICS
ECON 2750A
H.W. #2
Prof. K.C. Tran
Due Date:
Wednesday February 11, 2009
1. Let
 3  4
A

 5 1 
7 4 
B

5 k 
What value of k, if any, will make AB = BA?
2. Consider the situation of a mass layoff (i.e., a factory such down) where 1200 people
become unemployed and now begin a job search. In this case there are only 2 states:
Employed (E) and unemployed (U) with the initial vector
x 0T  E U   0 1200
Suppose that at any given period an unemployed person will find a job with probability
0.7 and will therefore remain unemployed with a probability of 0.3. Additionally, persons
who find themselves employed in any given period may loose their job with a probability
of 0.1 (and will have a 0.9 probability of remaining employed).
(a) Set up the transition probability matrix
(b) What will be the number of unemployed people after (i) 2 periods; (ii) 5 periods;
(iii) 10 periods?
(c) What is the steady-state level of unemployment? [By definition, the steady-state is
the situation where the new transition matrix found by raising the original matrix
to increasingly higher powers converges to a matrix where the elements in the
columns are identical].
3. Let X be any n  K matrix and define a projection matrix P  X ( X T X ) 1 X T and
let M  I  P
(a) What is the dimension of the matrix M? (Show your work!)
(b) Show that M is an idempotent matrix (You can take P as idempotent as we did in
class so that PP = P)
(c) Compute the trace of M
4. Given the following matrices
 1 0  2
A   3 0 5 
 1 2 4 
2 0 3 
B  1 5 0 
6 0  1
(a) Find the products of AT B and B T A
(b) Find the determinant for each matrix