Write the following National Income Model in the form Ax = b and solve using Cramer's Rule:

C=α+βY
I=γ+θr
Y=C+I

Where income(Y), consumption(C) and investment(I) are endogenous; the rate of interest(r) is exogenous and α, β, γ and θ are known constants. Also find the slope of the IS curve.

To solve this problem, you must start by transforming the system of equations into the form Ax = b. Where A is a matrix containing the coefficients on the endogenous variables, the size of A depends on the number of endogenous variables, in our case there are three endogenous variables which means A is a 3x3 matrix. Vector x contains the endogenous variables which we need to compute and vector b contains the known constants. The transformation can be done as follows:

Start by moving the endogenous variables to the left-hand side of the system as follows (take care with changing signs, the order of the variables and ...

Solution Summary

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