Consider the following national income model :

Y = C + I + Go

C = 215 + 0.59Y

4.2I = 197 + 0.22Y

Where Go= 90

(i) Identify the exogenous variable/s.

Convert this system of equations in matrix form.

(ii) What is the determinant of the coefficient matrix?

(Note: you can use either inversion or Cramer's rule to find the values of Y, C and I.)

(iii) What is the equilibrium value of Y?

(iv) What is the equilibrium value of C?

(v) What is the equilibrium value of I?

(vi) Find the Jacobian determinant to the test the existence of functional dependence between these three functions-

Y1= 12X1 + 8X2 + 3X3

Y2= 4X1 + 13X2 + 14X3

Y3= 10X1 + 11X2 + 17X3

What is the value of the Jacobian determinant ?