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,Pand
E, respectively. Suppose to produce one unit of output, Arequires 0.22 units of its own output, and 0.13
units of Mand 0.1 units of P. Making one unit of Mrequires 0.l9, 0.11, and 0.08 units of A,M, and P,
resp., and a unit of Pconsumes 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−Cand write it here; store it as [B] in your calculator.
1C. Use your calculator to find (I−C)−1and write it here. (Just use [B] and the “x−1” key)
1D. Let dbe the final demand vector. In terms of Cand 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 dinto your calculator as a matrix
(say [D]) and do an appropriate matrix multiplication.
1F. BONUS! It turns out that (I3+C+C2+C3+C4+C5)dis
81.154
55.618
131.592
. What is the connection
between this fact and your work in (1A-1E)?
quiz continues other side
