[1] Consider the following national income model where the goods and money market are modeled as follows: Goods market: Y=C+I+ Go C = 25 +0.5(Y-T) I= 0.4C -0.8r T= 10+ 0.2Y where Y, C, I, T, r are income, consumption, investment, taxes, and the real interest rate, respectively. Go = 20 is the government expenditure, which is determined exogenously. Money market: 0.4Y-0.2r Ma Ms = Mo Ma = Ms where Ma and M, are money demand and money supply equations. Money supply is exogenously determined at Mo = 39. a) In the national income model described above, what are the endogenous vari- ables? By comparing the number of endogenous variables and the number of equations, what can you say about whether the model can have a solution? b) Express the national income model in matrix form where the list of endoge- nous variables includes only Y, C, I,T,r. (You are asked to write down the matrix of coefficients, the vector of unknowns, and the vector of constants and how these three are related. You shouldn't solve the model.) c) Express the national income model in matrix form where the list of endoge- nous variables includes only Y, C. And solve the model. (You should find the values of all endogenous variables)
[1] Consider the following national income model where the goods and money market are modeled as follows: Goods market: Y=C+I+ Go C = 25 +0.5(Y-T) I= 0.4C -0.8r T= 10+ 0.2Y where Y, C, I, T, r are income, consumption, investment, taxes, and the real interest rate, respectively. Go = 20 is the government expenditure, which is determined exogenously. Money market: 0.4Y-0.2r Ma Ms = Mo Ma = Ms where Ma and M, are money demand and money supply equations. Money supply is exogenously determined at Mo = 39. a) In the national income model described above, what are the endogenous vari- ables? By comparing the number of endogenous variables and the number of equations, what can you say about whether the model can have a solution? b) Express the national income model in matrix form where the list of endoge- nous variables includes only Y, C, I,T,r. (You are asked to write down the matrix of coefficients, the vector of unknowns, and the vector of constants and how these three are related. You shouldn't solve the model.) c) Express the national income model in matrix form where the list of endoge- nous variables includes only Y, C. And solve the model. (You should find the values of all endogenous variables)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![[1] Consider the following national income model where the goods and money market
are modeled as follows:
Goods market:
Y=C+I+ Go
C = 25 +0.5(Y-T)
I= 0.4C -0.8r
T= 10+ 0.2Y
where Y, C, I, I,r are income, consumption, investment, taxes, and the real interest
rate, respectively. Go 20 is the government expenditure, which is determined
exogenously.
Money market:
Ma 0.4Y - 0.2r
Ms = Mo
Ma = Ms
where Ma and M, are money demand and money supply equations. Money supply
is exogenously determined at Mo = 39.
a) In the national income model described above, what are the endogenous vari-
ables? By comparing the number of endogenous variables and the number of
equations, what can you say about whether the model can have a solution?
b) Express the national income model in matrix form where the list of endoge-
nous variables includes only Y, C, I, T, r. (You are asked to write down the
matrix of coefficients, the vector of unknowns, and the vector of constants
and how these three are related. You shouldn't solve the model.)
c) Express the national income model in matrix form where the list of endoge-
nous variables includes only Y, C. And solve the model. (You should find the
values of all endogenous variables)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2F3ab6f7da-aae8-4035-b307-30b7a99bebc2%2F1r1e5ik_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[1] Consider the following national income model where the goods and money market
are modeled as follows:
Goods market:
Y=C+I+ Go
C = 25 +0.5(Y-T)
I= 0.4C -0.8r
T= 10+ 0.2Y
where Y, C, I, I,r are income, consumption, investment, taxes, and the real interest
rate, respectively. Go 20 is the government expenditure, which is determined
exogenously.
Money market:
Ma 0.4Y - 0.2r
Ms = Mo
Ma = Ms
where Ma and M, are money demand and money supply equations. Money supply
is exogenously determined at Mo = 39.
a) In the national income model described above, what are the endogenous vari-
ables? By comparing the number of endogenous variables and the number of
equations, what can you say about whether the model can have a solution?
b) Express the national income model in matrix form where the list of endoge-
nous variables includes only Y, C, I, T, r. (You are asked to write down the
matrix of coefficients, the vector of unknowns, and the vector of constants
and how these three are related. You shouldn't solve the model.)
c) Express the national income model in matrix form where the list of endoge-
nous variables includes only Y, C. And solve the model. (You should find the
values of all endogenous variables)
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