Applications - A Guide to MATLAB for Beginners and Experienced Users - page 169

A=

0.3000 0.1000 0.0500 0.2000

0.1000 0.2000 0.3000 0.3000

0.3000 0.5000 0.2000 0.3000

0.3000 0.2000 0.4500 0.2000

then as required,

sum(A)

ans =
1

1 1 1

That is, all the columns sum to 1, and

[V, D] = eig(A); D(1, 1)
p = V(:, 1)

ans =
1.0000

p=

0.2739
0.4768
0.6133
0.5669

shows that 1 is an eigenvalue of A withprice eigenvector p as shown.
Somewhat more realistic is the (static, linear) open Leontief model of an
economy, which takes labor, consumption, etc., into account. Let's illustrate
withan example. The following cell inputs an actual input-output
transactions table for the economy of the United Kingdom in 1963. (This
table is taken from Input-Output Analysis and its Applications by
R. O'Connor and E. W. Henry, Hafner Press, New York, 1975.) Tables such
as this one can be obtained from official government statistics. The table T
isa10 × 9 matrix. Units are millions of Britishpounds. The rows represent
respectively, agriculture, industry, services, total inter-industry, imports,
sales by final buyers, indirect taxes, wages and profits, total primary inputs,
and total inputs. The columns represent, respectively, agriculture, industry,
services, total inter-industry, consumption, capital formation, exports, total
final demand, and output. Thus outputs from each sector can be read off
along a row, and inputs into a sector can be read off along a column.