2. A two-sector macro-economic model satisfies the following structural equations:Y = C + I∗C = aY + bwhere 0 < a < 1 and b > 0 are parameters and I∗ denotes investment.(a) What are the exogenous and endogenous variables in this model? (b) Re-arrange this system of equations to express the endogenous variables in terms of the exogenous variables and parameters. (c) Express this system of equations in the matrix form Ax = b. (d) Show that the inverse of matrix A exists.
2. A two-sector macro-economic model satisfies the following structural equations:Y = C + I∗C = aY + bwhere 0 < a < 1 and b > 0 are parameters and I∗ denotes investment.(a) What are the exogenous and endogenous variables in this model? (b) Re-arrange this system of equations to express the endogenous variables in terms of the exogenous variables and parameters. (c) Express this system of equations in the matrix form Ax = b. (d) Show that the inverse of matrix A exists.
Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter1: Introducing The Economic Way Of Thinking
Section: Chapter Questions
Problem 7SQP
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Question
2. A two-sector macro-economic model satisfies the following structural equations:
Y = C + I
∗
C = aY + b
where 0 < a < 1 and b > 0 are parameters and I
∗ denotes investment.
(a) What are the exogenous and endogenous variables in this model?
(b) Re-arrange this system of equations to express the endogenous variables in terms of the exogenous variables and parameters.
(c) Express this system of equations in the matrix form Ax = b.
(d) Show that the inverse of matrix A exists.
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