Math 205 A B Quiz 02 (Remake) Worksheet - Bates College - 2012
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1Quiz 02 (remake) page 1
09/26/2012
Math 205 A B
Name
1. Suppose an economy has just three sectors C, N , S. Suppose that C consumes 20% of its own output while the rest of
C’s output is divided equally for consumption by sectors N and S. Suppose N consumes 70% of its own product, S consumes
20% of N ’s output and the remainder of N ’s output is used by C. Finally, of what is produced by S, 90% is taken by N and
the rest is used by C (so S takes none of its own output).
1A: In the space below, give both the exchange table for this economy and the corresponding system of equations that
you need to solve in determining the equilibrium prices P
, P
and P
for this economy.
C
N
S
1B: Find the set of equilibrium prices P
, P
and P
, if given that P
= 100 million dollars. Show any RREF’d matrices
C
N
S
S
involved in your solution.
1C: Find the set of equilibrium prices P
, P
and P
, if given that the price N pays C for what N consumes of C’s output
C
N
S
is 80 million dollars.
4
5
1 3
11
1 0
1 0
3
4
8
4 4
12
0 1
1 0
1
2. Let A =
and s =
. It’s a fact that RREF(A|s) is
.
4
1
5 3
5
0 0
0 1
2
1
2
3 1
1
0 0
0 0
0
2A. Find in parametric vector form all solutions to Ax = s.
2B. Find a non-trivial solution x to Ax = 0 or explain why there are none.
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