Question

Consider the simple macroeconomic model described by the three equations

(i) Y=C+A0
​(ii) C=a+b(Y−T)
(iii) T=d+tY
Here Y is GDP, C is consumption, T is tax revenue, A0 is the constant (exogenous) autonomous expenditure, and a,b,d, and t are all positive parameters. Find the equilibrium values of the endogenous variable Y,C, and T by writing the equations in matrix form and applying Cramer's rule.

Answer 1

To find the equilibrium values of GDP, consumption, and taxes in a simple macroeconomic model, one can set up the system of equations based on the Keynesian cross model and solve using Cramer's rule.

Step-by-step explanation:

The question involves finding the equilibrium values of GDP (Y), consumption (C), and taxes (T) using a macroeconomic model within the context of an expenditure-output or Keynesian cross model. To solve for these equilibrium values algebraically, you would typically set up an equation where aggregate expenditures equal output, AE = Y. For instance, using the parameters given in the examples, you could set up an equation like C + I + G + X - M = Y, with C as consumption, I as investment, G as government spending, X as exports, and M as imports (a function of Y and T).

Once the relevant equations are established, solving for equilibrium Y, C, and T can be accomplished by representing these equations in matrix form and applying Cramer's rule. However, the actual numerical solution would require specific values for the parameters and the algebraic setup of the system of equations, which would then be solved using determinants as outlined by Cramer's rule.