Determine the sectoral gross outputs if the final demand

Question

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?

Answer 1

Please consider the inter-sectoral transaction table (illustrated in the problem) for the United States, aggregated from data provided by BEA, make use of table (after redefinition) 2011. The sectors are Agriculture (AG), Construction and Mining (comprising utilities) (C&M), Manufacturing (Manu) and Services (Ser) (not including local, state and the federal government). 1) Employ the data and make the matrix of inter-sectoral input coefficients and determine total sectoral outs Q. Form a diagonal matrix having the sectoral outputs on the major diagonal and zero everywhere else. Multiply the inter-sectoral transaction matrix T via the inverse of this matrix. This provides you matrix A. 2) Find out the sectoral gross outputs if the final demand for just the Agri-cultural sector's products rises by 3 %. 3) Determine the growth rate of the economy? 4) Repeat parts (2) and (3) for other sectors. Rank the sector based on their impact on economy.