Use the counting rule to find the number of degrees of freedom in the following macroeconomic model (which is studied further in Problem 12.11.6):
(i) Y = C + I + G
(ii) C = F(Y,T,r)
(iii) I = f (Y, r)
(The symbols have the same interpretation as in Example 1. We assume that F and f are specified functions of their respective arguments.)
EXAMPLE 1
Consider the macroeconomic model described by the system of equations
(i) Y = C + I + G
(ii) C = f (Y - T )
(iii) I = h(r)
(iv) r = m(M)
Where f , h, and m are given functions, Y is national income, C is consumption, I is investment, G is public expenditure, T is tax revenue, r is the interest rate, and M is the money supply (or more exactly, the quantity of money in circulation). How many degrees of freedom are there?