Question 12.10.1: Consider the macroeconomic model described by the system of ......
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 GDP, C is consumption, I is investment, G is public expenditure, T is tax revenue, r is the interest rate, and M is the quantity of money in circulation. How many degrees of freedom are there?
The number of variables is seven and the number of equations is four, so according to the counting rule there should be 7 − 4 = 3 degrees of freedom. Usually macroeconomists regard M, T, and G as the exogenous (free) variables. Then the system will in general determine the endogenous variables Y, C, I, and r as functions of M, T, and G.^{10}
^{10} For a further analysis of this model, see Example 12.11.3. For a discussion of exogenous and endogenous variables, see Section 12.11.