SOLUTION: an economy is based on three sectors: real estate, energy, and manufacturing. Production of 1 unit of real estate requires 0.2 units of real estate and 0.4 units of energy. Produ

Question 1116904: an economy is based on three sectors: real estate, energy, and manufacturing. Production of 1 unit of real estate requires 0.2 units of real estate and 0.4 units of energy. Production of 1 unit of energy requires 0.2 units of energy and 0.4 units of manufacturing. Production of 1 unit of manufacturing requires 0.1 units of real estate, 0.1 units of energy, and 0.3 units of manufacturing.
a) Set up the technology matrix (input-output matrix)
b) What gross production is necessary to meet an external demand for 20 units of real estate, 10 units of energy, and 30 units of manufactoring?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the way i see this problem is as follows:

R = outside real estate
r = inside real estate required.
E = outside energy
e = inside energy required.
M = outside manufacturing
m = inside manufacturing required.

you are given:

Production of 1 unit of real estate requires 0.2 units of real estate and 0.4 units of energy. Production of 1 unit of energy requires 0.2 units of energy and 0.4 units of manufacturing. Production of 1 unit of manufacturing requires 0.1 units of real estate, 0.1 units of energy, and 0.3 units of manufacturing.

from that, you get:

R = .2r + .4e
E = .2e + .4m.
M = .1r + .1e + .3m

you are asked:

a) Set up the technology matrix (input-output matrix)
b) What gross production is necessary to meet an external demand for 20 units of real estate, 10 units of energy, and 30 units of manufactoring?

in order to make 20 units of R, you would require:

20 * (.2r + .4e) which is equal to 4r + 8e

in order to make 10 units of E, you would require:

10 * (.2e + .4m) = 2e + 4m

in order to make 30 units of M, you would require:

30 * (.1r + .1e + .3m) = 3r + 3e + 9m

these requirements are summarized below:

20R = 4r + 8e
10E = 2e + 4m
30M = 3r + 3e + 9m

the total resource required would be 7r + 13e + 13m

i don't see how this problem involves a matrix, so this may not be of help but what i did does provide an answer and does appear to be logically correct, at least from the way i'm looking at it.

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