Solve Y=C+1o+Go, C= a+b(Y-T), T= d+tY using matrix inversion, and again by using Cramer's Rule CISE 5.60ave seen from ttion for any linear-equationfor testing the existence of a uniqueise available. In addition, it should be noted thiable method, which affords no means of analyticaltion, the matrix-inversion method and Cramer's rule do provide theexpressions x* = A'd and x = 14,\/\4). Such analytical expressions ofoperations on the solution as written, if called for.useful not only because they are in themselves a summary statement of theprocedure, but also because they make possible the performance of furthUnder certain circumstances, matrix methods can even claim a comptage, such as when the task is to solve at the same time several equationan identical coefficient matrix A but different constant-term vectors. Inelimination-of-variable method would require that the computationalpeated each time a new equation system is considered. With the matrix-however, we are required to find the common inverse matrix A¹ only orinverse can be used to premultiply all the constant-term vectors pertainequation systems involved, in order to obtain their respective soluticcomputational advantage will take on great practical significance whsolution of the Leontief input-output models in Sec. 5.7.Solve the national-income model in Exercise 3.5-1:(a) By matrix inversion (b) By Cramer's rule(List the variables in the order Y, C, T.)2. Solve the national-income model in Exercise 3.5-2:(a) By matrix inversion (b) By Cramer's rule(List the variables in the order Y, C, G.)fo E 3.5As a check on our calculation, we can add the C* expression in (3.25) to (To+Go) andverify that the sum is equal to the Y* expression in (3.24).This model is obviously one of extreme simplicity and crudity, but other models ofnational-income determination, in varying degrees of complexity and sophistication, canbe constructed as well. In each case, however, the principles involved in the constructionand analysis of the model are identical with those already discussed. For this reason, weshall not go into further illustrations here. A more comprehensive national-income model.involving the simultaneous equilibrium of the money market and the goods market, will bediscussed in Sec. 8.6.C1 Given the following model:Y = C + lo + GoC = a + b(Y - T)T=d+tY(a>0,(d>0,Chapter 3 Equilibrium Analysis in Economics 470

GivenHere Y, C, and T are endogenous variables. To form the coefficient matrix, write the endogenous…

Answered: Solve the (a) By matrix inversion (List…

Solve the (a) By matrix inversion (List the variables in the order Y, C, T.) national-income model in Exercise 3.5-1: (b) By Cramer's rule

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Question

Solve Y=C+1o+Go, C= a+b(Y-T), T= d+tY using matrix inversion, and again by using Cramer's Rule

CISE 5.6
0
ave seen from t
tion for any linear-equation
for testing the existence of a unique
ise available. In addition, it should be noted th
iable method, which affords no means of analytical
tion, the matrix-inversion method and Cramer's rule do provide the
expressions x* = A'd and x = 14,\/\4). Such analytical expressions of
operations on the solution as written, if called for.
useful not only because they are in themselves a summary statement of the
procedure, but also because they make possible the performance of furth
Under certain circumstances, matrix methods can even claim a comp
tage, such as when the task is to solve at the same time several equation
an identical coefficient matrix A but different constant-term vectors. In
elimination-of-variable method would require that the computational
peated each time a new equation system is considered. With the matrix-
however, we are required to find the common inverse matrix A¹ only or
inverse can be used to premultiply all the constant-term vectors pertain
equation systems involved, in order to obtain their respective solutic
computational advantage will take on great practical significance wh
solution of the Leontief input-output models in Sec. 5.7.
Solve the national-income model in Exercise 3.5-1:
(a) By matrix inversion (b) By Cramer's rule
(List the variables in the order Y, C, T.)
2. Solve the national-income model in Exercise 3.5-2:
(a) By matrix inversion (b) By Cramer's rule
(List the variables in the order Y, C, G.)
fo

E 3.5
As a check on our calculation, we can add the C* expression in (3.25) to (To+Go) and
verify that the sum is equal to the Y* expression in (3.24).
This model is obviously one of extreme simplicity and crudity, but other models of
national-income determination, in varying degrees of complexity and sophistication, can
be constructed as well. In each case, however, the principles involved in the construction
and analysis of the model are identical with those already discussed. For this reason, we
shall not go into further illustrations here. A more comprehensive national-income model.
involving the simultaneous equilibrium of the money market and the goods market, will be
discussed in Sec. 8.6.
C
1 Given the following model:
Y = C + lo + Go
C = a + b(Y - T)
T=d+tY
(a>0,
(d>0,
Chapter 3 Equilibrium Analysis in Economics 47
0<b<1) [T: taxes]
0<t<1) [t: income tax rate)
(a) How many endogenous variables are there?
(b) Find Y*, T*, and C*.
income model be:

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