Math 205a Quiz 09 Worksheet - Bates College - 2008

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Math 205A
Quiz 09 page 1
March 28, 2008
NAME
1. Suppose an economy has three producing sectors: agriculture, meats, and processed foods. The open
sector consists of people who just consume (“eat”) all these foods. The four sectors are thus A, M, P and
E, respectively. Suppose to produce one unit of output, A requires 0.22 units of its own output, and 0.13
units of M and 0.1 units of P . Making one unit of M requires 0.l9, 0.11, and 0.08 units of A, M, and P ,
resp., and a unit of P consumes 0.1, 0.07 and 0.3 units of A, M, and P , resp. The final demand by the E
sector is 40, 30, and 80 units of A, M, and P , resp.
1A. Find the consumption matrix C.
1B. Find I
C and write it here; store it as [B] in your calculator.
1
1
1C. Use your calculator to find (I
C)
and write it here. (Just use [B] and the “x
” key)
1D. Let d be the final demand vector. In terms of C and d, what is the equation which we set up to
find the production vector x?
1E. Find the production vector x. (Hint: put the final demand vector d into your calculator as a matrix
(say [D]) and do an appropriate matrix multiplication.
81.154
 . What is the connection
2
3
4
5
55.618
1F. BONUS! It turns out that (I
+ C + C
+ C
+ C
+ C
) d is
3
131.592
between this fact and your work in (1A-1E)?
quiz continues other side

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