Posted: October 20th, 2022

JF Nadeau
30/09/2022
Question 1
A) Given your knowledge of the dimensions of the tables U of uses and resources V, construct the table of uses and
resources in the R software .
**DATE OF DELIVERY:** October 20, 2022
D) Using the appropriate summation vector i , construct the total output vector x of each of the industries.
Figure 1: Table of uses and resources
Consider a commodity input-output model by industry with m = 3 commodities and n = 2 industries.
E) What is the value added in each industrial sector?
C) Calculate the final demand vector e for each of the commodities.
1
G) Given your answer in F), what is the total output of each sector that is needed to satisfy a final demand of $1 for
commodity 2?
B) Using the appropriate summation vector i , construct the total output vector q of each of the commodities.
** Submit only your R code, with your answers inserted as comments **
F) Find, for this model, the table of total industry requirements by commodity.
Team duty 1
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Question 3
Question 2
A1
and the matrix of technical coefficients
ÿ
ÿ
ÿ
Let us first assume that the household sector is part of exogenous final demand.
Now assume that we close this model with respect to households, i.e. households are no longer considered part of
exogenous final demand.
P =
f) Calculate the new inter-industry transaction matrix resulting from the change in final demand for the output of sector
2 described in d). By how much did labor income in sector 1 increase as a result of the change in final demand?
| {z} 2
× 2
| {z} 3
× 3
0.25 0.3
0.25 0.25 0.4
ÿ
a) Build the interindustrial transaction matrix Z0
| {z} 3
× 3
Given the following data on an economy with 2 industrial sectors
0.15 0.20 0.5
c) Build the inter-industry transaction matrix Z1
g) Consider the matrix P which describes the proportion of wages in each industrial sector (including the household
sector) that goes to each of the 4 major categories of workers in this economy
0.35 0.25 0.1
2
b) Now assume that the other final demand for the output of sector 2 increases by 20 percent. What will be the
required change in the production of Sector 1 to meet this additional demand?
d) Now assume that the other final demand for the output of sector 2 increases by 20 percent. What will be the
required change in the production of sector 1 to satisfy this additional demand, given that the households are now
considered endogenous to the response of the model?
0
e) Is your answer obtained in d) different from that obtained in b)? How do you explain this result, considering that the
change in final demand is the same in both questions?
corresponding
Consider a commodity input-output model by industry with m = 4 commodities and n = 3 industries. We know the total
output vector for each commodity q,
| {z} 2
× 2
ÿ
ÿ
which correspond to the closed model for households.
Identify the wages received by each category of worker in each sector, following the change in final demand described
in d). For example, how much the category 1 worker receives in salary in sector 1, how much he receives in sector 2
and how much he receives from households.
ÿ
ÿ
and the matrix of technical coefficients A0
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Question 4
## [4,] 0.11009174 0.05704698 0.23809524
yt = A · k
[,2] [,3] [,4]
## [1,] 1.1640420 0.07748173 0.08242163 0.2501780
=
## [1,] 107
## [3,] 0.09174312 0.04362416 0.06547619
(1)
## [1,] 0.18348624 0.04026846 0.10714286
4. Value added in each industrial sector will
q
##
B
[,1]
Consider the Solow model composed of the following equations
3
=
##
## [4,] 0.18984654 0.10989512 0.12006687 1.3283342
Finally, the matrix B
[,1]
1. The U job board
is given by
##
## [3,] 149
## [2,] 0.09873774 1.13084469 0.13083104 0.1285170
## [3,] 0.1821774 0.14792980 0.19733828 1.1864668
D
(2)
## [1,] 1.24603615 0.07675608 0.08144848 0.1859430
## [2,] 149
5. the market share matrix D,
[,1]
| {z}
[,1]
[,2] [,3] [,4]
## [2,] 0.04587156 0.10067114 0.07142857
[,3]
3. The total industrial production of each industry x
it = s · yt
Lcc
and the table of total industry requirements by convenience, which we represent by Lic
Lic
[,2]
the table of total requirements convenience by convenience, which we represent by Lcc,
2. The Resource Table V
Using this information, calculate
| {z}
## [4,] 170
##
## [3,] 0.13273021 0.06737473 1.06942959 0.1146312
B
(3)
## [2,] 0.3211313 1.15945909 1.12201606 0.3207806
that
qj
m×n xj
tÿ1
kt = it + (1 ÿ ÿ)ktÿ1
vij
a
n×m
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A) Assume s = 0.2, A = 2, ÿ = 0.1 and ÿ = 0.3. Find the values of c
Has the consumption increased or decreased compared to your answer in A)?
What is, in %, the minimum increase in TFP that will allow consumption per person (a measure of the standard of living)
to remain at the level observed in A), despite the drop in the savings rate?
(5)
(6)
4
(4)
Calculate the new level of consumption per person in the steady state following this drop in the savings rate. Has the
consumption increased or decreased compared to your answer in A)?
ÿ at steady state. and there
wt = (1 ÿ ÿ) · yt
where s is the constant savings rate, ÿ is the share of capital in output, A is the level of total factor productivity (TFP)
and ÿ is constant capital depreciation. All variables except the interest rate Rt and the wage wt are expressed relative to
the total population, so for example, ct is the consumption per person in the economy.
B) Now assume that A = 3, ie there is a permanent increase in the level of TFP. Calculate the new level of consumption
per person at steady state as a result of this increase in TFP.
Rt = ÿ · A · k
C) Now assume that A = 2 but s = 0.15, ie there is a permanent decline in the savings rate.
yt = ct + it
tÿ1
ÿ
(aÿ1)
D) Assume again that A = 2 but s = 0.15, ie there is a permanent decline in the savings rate.
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