Below is the inter-sectoral transaction table for the United States, aggregated from data provided by BEA Use Table (after redefinition) 2011. The sectors are Agriculture (AG), Construction and Mining (including utilities)(C & M), Manufacturing (Manu), and Services (Ser) (excluding local, state, and federal government).1
4-Sector Input-Output Table of the U.S. ($1000)
|
|
AG
|
C & M
|
Manu
|
Ser
|
|
AG
|
82550
|
1109
|
246867
|
14595
|
|
C & M
|
9418
|
143422
|
653526
|
204375
|
|
Manu
|
100120
|
322107
|
1834966
|
868271
|
|
Ser
|
65865
|
213120
|
861584
|
4863250
|
The vector of Final Demand (FD) for the 4 sectors is
FD =
? 69980 ?
? 897154 ?
?1845577?
?850000 ?
(a) Use the data and prepare the matrix of inter-sectoral input coefficients. (Hint: use (13.16) and find total sectoral outs Q. Form a diagonal matrix with the sectoral outputs on the main diagonal and zero everywhere else. Multiply inter-sectoral transaction matrix T by the inverse of this matrix. This gives you matrix A)
(b) Determine the sectoral gross outputs if the final demand for only the Agri- cultural sector's products increases by 3 %. (Hint: create a unit matrix I of size 4. Calculate (I - A) and (I - A)-1. Note that you must get the original vector of output if you calculate (I - A)-1 F D)
1 Imports and exports are also excluded.
(c) What is the growth rate of the economy?
(d) Repeat parts (b) and (c) for other sectors. Rank sector based on their impact on the economy. Can this be determined by the column elements of (I - A)-1 that provides the direct and indirect output requirements per unit of final
demand?