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 simultaneous equations
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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 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...
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+IC= aY+bWhere 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.
2. Consider the National Income model given by the following equations. Y-C-I.-G, = 0 C-a-B(Y -...
2. Consider the National Income model given by the following equations. Y-C-I.-G, = 0 C-a-B(Y - T) = 0 T-y-SY=0 where Y, C, and T are endogenous variables and I., G., a, b, Y, 8 are exogenous and B and 8 are positive fractions. Use Cramer’s Rule to find the effect of a change in G, on Y and C.
Consider IS- LM Model Real Sector: Y C+IG C ab (1-t) Y I d-e t-income tax...
Consider IS- LM Model Real Sector: Y C+IG C ab (1-t) Y I d-e t-income tax rate i-rate of interest G Go Money Market: Md Ms Md kY - Ms Mo Mo - exogenous stock of money 1) Setup the system of solutions in general form, with variables vector in the following order: Y, C, I, i; (6 points) 2) Now, suppose we have the following values of parameters: a 10; b 0.7;t= 0.2; d 25; k 0.25;1 0.04; e...
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...
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...
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...
Consider IS-LM Model: Real Sector: Y=C+I+G C=a+b (1-t) Y I=d-ei G=GO t-income tax rate i- rate...
Consider IS-LM Model: Real Sector: Y=C+I+G C=a+b (1-t) Y I=d-ei G=GO t-income tax rate i- rate of interest Money Market: Ma=M Ma=ky-li M = Mo Mo - exogenous stock of money 1) Setup the system of solutions in general form, with variables vector in the following order: Y, C, I, i; (6 points) 2) Now, suppose we have the following values of parameters: a= 10; b = 0.7; t = 0.2; d = 25; k = 0.25; 1 = 0.04;...
4. (28 pts) Consider the following macroeconomic model: Y C M = C + Io +...
4. (28 pts) Consider the following macroeconomic model: Y C M = C + Io + Xo - M = a +bY = u +mY a> 0 and 0 <b<1 u> 0 and 0 <m < 1 The three endogenous variables are Y (income), C (consumption), and M (imports). The variables I. (investments) and X. (exports) are exogenous. Also, a, b, u and m are exogenous constants satisfying the restrictions presented above. (a) Write this system as a 3 x...
4. Points = 18. Consider IS-LM Model: Real Sector: Y=C+I+G C = a +b (1-t) Y...
4. Points = 18. Consider IS-LM Model: Real Sector: Y=C+I+G C = a +b (1-t) Y I=d-ei G=Go t-income tax rate i-rate of interest Money Market: Ma=M Ma= kY-li Mg = Mo Mo - exogenous stock of money 1) Setup the system of solutions in general form, with variables vector in the following order: Y, C, I, i; (6 points) 2) Now, suppose we have the following values of parameters: a = 10; b = 0.7; t = 0.2; d...
2. Consider the National Income model given by the following equations. Y-C-I.-G, = 0 C-a-B(Y - T) = 0 T-y-SY=0 where Y, C, and T are endogenous variables and I., G., a, b, Y, 8 are exogenous and B and 8 are positive fractions. Use Cramer’s Rule to find the effect of a change in G, on Y and C.
Consider IS- LM Model Real Sector: Y C+IG C ab (1-t) Y I d-e t-income tax rate i-rate of interest G Go Money Market: Md Ms Md kY - Ms Mo Mo - exogenous stock of money 1) Setup the system of solutions in general form, with variables vector in the following order: Y, C, I, i; (6 points) 2) Now, suppose we have the following values of parameters: a 10; b 0.7;t= 0.2; d 25; k 0.25;1 0.04; e...
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...
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...
Consider IS-LM Model: Real Sector: Y=C+I+G C=a+b (1-t) Y I=d-ei G=GO t-income tax rate i- rate of interest Money Market: Ma=M Ma=ky-li M = Mo Mo - exogenous stock of money 1) Setup the system of solutions in general form, with variables vector in the following order: Y, C, I, i; (6 points) 2) Now, suppose we have the following values of parameters: a= 10; b = 0.7; t = 0.2; d = 25; k = 0.25; 1 = 0.04;...
4. (28 pts) Consider the following macroeconomic model: Y C M = C + Io + Xo - M = a +bY = u +mY a> 0 and 0 <b<1 u> 0 and 0 <m < 1 The three endogenous variables are Y (income), C (consumption), and M (imports). The variables I. (investments) and X. (exports) are exogenous. Also, a, b, u and m are exogenous constants satisfying the restrictions presented above. (a) Write this system as a 3 x...
4. Points = 18. Consider IS-LM Model: Real Sector: Y=C+I+G C = a +b (1-t) Y I=d-ei G=Go t-income tax rate i-rate of interest Money Market: Ma=M Ma= kY-li Mg = Mo Mo - exogenous stock of money 1) Setup the system of solutions in general form, with variables vector in the following order: Y, C, I, i; (6 points) 2) Now, suppose we have the following values of parameters: a = 10; b = 0.7; t = 0.2; d...
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