Consider the following national income model :

Y = C + I + G_o

C = 110 + 0.48Y

3.5I = 167 + 0.18Y

Where G_o = 183

(i) Identify the exogenous variable/s.

if there are more than one variable, separate each variable with a comma

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 = 4X1 + 6X2 + 7X3

Y₂ = 10X1 + 5X2 + 8X3

Y₃ = 6X1 + 10X2 + 19X3

What is the value of the Jacobian determinant?

(vii) Under pure competition, the supply curve for a certain product is given by: P= Q² + 100, the demand curve is given by: Q = 40 - (1/25)P.

Using integration, calculate the consumer surplus.

Using integration, calculate the producer surplus.