Application of Matrix to National Income Model
The equilibrium of consumption C, and Income Y for the Simple two sector model satisfy the structural equation;
Y= C+I
C= aY+b
Where a and b are parameters 0<a<1 and b>0 and I denote investment. Express the system in a matrix form and hence express Y and C in terms of a and b and give an economic interpretation of the inverse matrix.
Homework Answers
National Income Model - Application of Matrix Algebra Consider the following three-sector national income determination model:...
National Income Model - Application of Matrix Algebra Consider the following three-sector national income determination model: C = 30 + 0.75 (Y − T) T = 10 + 0.3Y I = 250 G = 100 Determine the exogenous and endogenous variables in the system. Solve the model presented in the above system of equations using the determinant and the inverse matrix method to find the equilibrium values of unknown variables. Verify your solution in part (b) above by solving these...
National Income Model - Application of Matrix Algebra Consider the following three-sector nationa...
National Income Model - Application of Matrix Algebra Consider the following three-sector national income determination model: C = 30 + 0.75 (Y − T) T = 10 + 0.3Y I = 250 G = 100 Determine the exogenous and endogenous variables in the system. Solve the model presented in the above system of equations using the determinant and the inverse matrix method to find the equilibrium values of unknown variables. Verify your solution in part (b) above by solving these...
1. Points = 18. Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C...
1. Points = 18. Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=Go T=f+jY 0<b<1 (<r<1 a> 0 in mln dollars; k>0 in mln dollars; Go >O in mln dollars p> 0 in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y) in reduced form (3 points); 3) If we know the...
Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b...
Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=GO T=f+jY <b<1 (<r<1 a>0 in mln dollars; k>O in mln dollars; Go >O in mln dollars fo in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y*) in reduced form (3 points); 3) If we know the parameters of the system, find the...
please, i need answeer for all 4 questions Consider National-Income Model: National Income: Consumption: Investment: Government...
please, i need answeer for all 4 questions
Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=Go T=f+jY 0<b<1 0<x<1 a> 0 in mln dollars; k>0 in mln dollars; Go > in mln dollars f> 0 in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y) in reduced form (3 points); 3)...
USU.US CUJL 1.ULTIUZULUV.CUIT 1. Points = 18 Consider National-Income Model: National Income: Consumption: Investment: Government Sector:...
USU.US CUJL 1.ULTIUZULUV.CUIT 1. Points = 18 Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=Go T=f+jY 0<b<1 0<r<1 a> 0 in mln dollars; k>0 in mln dollars; Go >O in mln dollars f> 0 in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y) in reduced form (3 points); 3) If...
in the macroeconomics model below matrix In the macroeconomic model below, Y is aggregate output, C...
in the macroeconomics model below matrix
In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, Io is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and T are en dogenous, Go, lo, and t are exogenous, and a, b, and k are parameters. Express this system of equations in a matrix form, clearly wrting out and...
b) Let a national-income model for a hypothetical economy be presented as: ? = ? +...
b) Let a national-income model for a hypothetical economy be presented as: ? = ? + ?0+ ?0 ? = 3 + 3? 1/2 ?0 = 4 ??? ?0 = 3 where ?, ?, ?0 , ?0 and ?0, respectively represent income, consumption, autonomous consumption, autonomous investment and autonomous government expenditure in trillions (RM). i) Give the economic meaning of the parameter b. ii) Solve for the endogenous variables of the model. iii) Now, if ?0 = 3.75, ?0= 6...
Consider the simple macro model described by the following equations Y= C + A0 C =...
Consider the simple macro model described by the following equations Y= C + A0 C = a + b(Y – T) T = d + tY Where Y is income, T is tax revenue, C is consumption, A0 is the constant autonomous expenditure, and a, b, d, and t are all positive parameters. Find the equilibrium values of the endogenous variables Y, C, and T by writing the equations in matrix form and applying Cramer’s rule.
We are now going to go to the national income model, and add a financial market...
We are now going to go to the national income model, and add a financial market to it. In thefinancial markets, as a nation, we borrow to invest. This means that the demand for investment,I, is now endogenous, and is a function of the real interest rate,R0, which is exogenous. The15 system of equations is nowY“C`I`G0C“α`βpY ́Tq pαą0; 0ăβă1qT“γ`δYpγą0; 0ăδă1qI“ ́θR0pą0;θą0q.(a) Solve the system of equations and get the equilibrium expressions of the endogenous variablesin terms of the exogenous variables...
1. Points = 18. Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=Go T=f+jY 0<b<1 (<r<1 a> 0 in mln dollars; k>0 in mln dollars; Go >O in mln dollars p> 0 in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y) in reduced form (3 points); 3) If we know the...
Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=GO T=f+jY <b<1 (<r<1 a>0 in mln dollars; k>O in mln dollars; Go >O in mln dollars fo in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y*) in reduced form (3 points); 3) If we know the parameters of the system, find the...
please, i need answeer for all 4 questions
Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=Go T=f+jY 0<b<1 0<x<1 a> 0 in mln dollars; k>0 in mln dollars; Go > in mln dollars f> 0 in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y) in reduced form (3 points); 3)...
USU.US CUJL 1.ULTIUZULUV.CUIT 1. Points = 18 Consider National-Income Model: National Income: Consumption: Investment: Government Sector: Taxes: Y=C+I+G C = a + b (Y-T) I=k+rY G=Go T=f+jY 0<b<1 0<r<1 a> 0 in mln dollars; k>0 in mln dollars; Go >O in mln dollars f> 0 in mln dollars; 0<j<1 1) Discuss in words the meaning of each of the equations in the model (3 points); 2) Find the equilibrium level of GDP (Y) in reduced form (3 points); 3) If...
in the macroeconomics model below matrix
In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, Io is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and T are en dogenous, Go, lo, and t are exogenous, and a, b, and k are parameters. Express this system of equations in a matrix form, clearly wrting out and...
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