Consider the following simple national-income model: Y=C+G C = 30 +0.5(Y-T) T = 10+tY Where the...

 

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Consider the following simple national-income model: Y=C+G C = 30 +0.5(Y-T) T = 10+tY Where the endogenous variables are national income (Y), consumption (C), and taxes (T), and the exogenous variables are government spending (G) and the income tax rate (t), where 0 < t < 1. a) Set up the model in matrix form. Call A the 3x3 matrix of coefficients. [5 marks] b) Compute the determinant of A and explain what the determinant equals to zero implies for our system of equations. [10 marks] c) Find the equilibrium consumption Cand equilibrium taxes T* using Cramer's rule. [10 marks] d) Find the impact of a rise in government spending G on equilibrium consumption C* and equilibrium taxes T*. Interpret your results. [5 marks] e) Is matrix A positive or negative definite (or neither of the two)? [5 marks] Consider the following simple national-income model: Y=C+G C = 30 +0.5(Y-T) T = 10+tY Where the endogenous variables are national income (Y), consumption (C), and taxes (T), and the exogenous variables are government spending (G) and the income tax rate (t), where 0 < t < 1. a) Set up the model in matrix form. Call A the 3x3 matrix of coefficients. [5 marks] b) Compute the determinant of A and explain what the determinant equals to zero implies for our system of equations. [10 marks] c) Find the equilibrium consumption Cand equilibrium taxes T* using Cramer's rule. [10 marks] d) Find the impact of a rise in government spending G on equilibrium consumption C* and equilibrium taxes T*. Interpret your results. [5 marks] e) Is matrix A positive or negative definite (or neither of the two)? [5 marks]