[11] Consider the following national income model Y = C + Io + Go C = 60+ a(Y-T) T = 30+tY where Y is the national income (GDP), C is consumption, Io and Go are investment and government expenditures that these two variables are exogenously given (i.e. they are some given constants). On the other hand, C is determined by the second equation so it's an endogenous variable. Similarly, total taxes collected in the economy (7) is also endogenously determined. a) What is the economic interpretation of the parameters a and t? b) Express this model in matrix form. As we saw in class, there are different ways to put the system into a matrix form. I ask you to form in two different ways: • obtain a matrix form in which the vector of unknowns contains the vari- ables y, C, T. • obtain a matrix form in which the vector of unknowns contains only the variables Y and C. c) Find the values of the endogenous variables by matrix inversion. For this part suppose Io = 31, Go = 20, a = 0.9, and t= 0.2. d) Now assume that the nation maintains a balanced budget, that is, the govern- ment spending is exactly equal to the total tax revenues. Express this model in matrix form.

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