using python
2. Suppose that the economy is described by the following system of equations:
Y=C+I+G
C=Co+b(1-t)Y
I=Io-er
G=Go
MofY-gr.
(1)
The endogenous variables in system (1) are Y, C, I, and r. The exogenous variables are the
three levels of autonomous spending, Co, Io, and Go, and the constant stock of money, Mo.
The simultaneous solution of the first four equations in system (1) will define the set of
combinations of values of Y and r that establishes equilibrium in the goods market; the locust of
which is the IS Curve.
The last equation in system (1) defines the set of values for Y and r that that yields equilibrium
in the money market; the locust of which defines the LM Curve.
a. Use SymPy to define the system in the matrix form Ax = b, where x is a vector of the
endogenous variables and b is a vector of the exogenous variables.
b. What is the determinant of A? Is the matrix A invertible?
c. Using SymPy and linsolve solve the system, i.e., derive the equilibrium values of the
endogenous variables.
d. What is the ceteris paribus impact of a change in autonomous consumption on equilibrium
output?
e. What is the ceteris paribus impact of a change in the stock of money on the equilibrium interest
rate?
