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
The solution is very detailed and solved a complex problem. The steps however are easy to understand. The response does a great job of explaining a very complex problem in very simple steps. Make sure that you refer to the attachment while reading the response. This is a matrices problem and in particular using the Cramer's Rule to solve a National Income Model. Response is concise yet well explained.
... The key issue is the failure to recognize different types of matrices: there are three matrix structures, pure (functional), balanced, and project matrices. ...
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