Consider the following macroeconomic model: Y=C+ Io + Go C=a+b(Y-T) T=d+tY Where the endogenous variables are Y,C and T, while the exogenous variables are G, and I. The parameters are such that a>0,d > 0,0

Consider the following macroeconomic model: Y=C+ Io + Go C=a+b(Y-T) T=d+tY Where the endogenous variables are Y,C and T, while the exogenous variables are G, and I. The parameters are such that a>0,d > 0,0

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider the following macroeconomic model:
Y = C + Io + Go
C = a + b(Y-T)
T = d+tY
Where the endogenous variables are Y, C and T, while the exogenous
variables are G₁ and I. The parameters are such that a > 0,d>0,0<b<
1,0 < t < 1.
a) Set up the model in matrix form.
b) Find the inverse of the matrix of parameters.
c) Use Cramer's rule to find equilibrium income Y* and equilibrium taxes
T'.
d) Find and discuss the impact of a rise in government spending G, on
equilibrium income Y".
e) What does t represents in the model? What is the impact of a rise in t
on equilibrium income Y* and on equilibrium taxes 7*? Explain
[Suggestion: to make computation easier, feel free to group together
some variables, e.g. call k = (a + Io + Go)]

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