[11] Consider the following national income model Y = C + Io + Go C = 60+ a(Y-T) T = 30+tY where Y is the national income (GDP), C is consumption, Io and Go are investment and government expenditures that these two variables are exogenously given (i.e. they are some given constants). On the other hand, C is determined by the second equation so it's an endogenous variable. Similarly, total taxes collected in the economy (7) is also endogenously determined. a) What is the economic interpretation of the parameters a and t? b) Express this model in matrix form. As we saw in class, there are different ways to put the system into a matrix form. I ask you to form in two different ways: • obtain a matrix form in which the vector of unknowns contains the vari- ables y, C, T. • obtain a matrix form in which the vector of unknowns contains only the variables Y and C. c) Find the values of the endogenous variables by matrix inversion. For this part suppose Io = 31, Go = 20, a = 0.9, and t= 0.2. d) Now assume that the nation maintains a balanced budget, that is, the govern- ment spending is exactly equal to the total tax revenues. Express this model in matrix form.

Economics:
10th Edition
ISBN:9781285859460
Author:BOYES, William
Publisher:BOYES, William
Chapter9: Aggregate Expenditures
Section: Chapter Questions
Problem 7E
icon
Related questions
Question
Show full answers to the questions and steps to this exercise
[11] Consider the following national income model
Y = C + Io + Go
C = 60+ a(Y-T)
T = 30+tY
where Y is the national income (GDP), C is consumption, Io and Go are investment
and government expenditures that these two variables are exogenously given (i.e.
they are some given constants). On the other hand, C is determined by the second
equation so it's an endogenous variable. Similarly, total taxes collected in the
economy (T) is also endogenously determined.
a) What is the economic interpretation of the parameters a and t?
b) Express this model in matrix form. As we saw in class, there are different
ways to put the system into a matrix form. I ask you to form in two different
ways:
obtain a matrix form in which the vector of unknowns contains the vari-
ables Y, C, T.
obtain a matrix form in which the vector of unknowns contains only the
variables Y and C.
Find the values of the endogenous variables by matrix inversion. For this part
suppose Io = 31, Go = 20, a = 0.9, and t = 0.2.
d) Now assume that the nation maintains a balanced budget, that is, the govern-
ment spending is exactly equal to the total tax revenues. Express this model
in matrix form.
Transcribed Image Text:[11] Consider the following national income model Y = C + Io + Go C = 60+ a(Y-T) T = 30+tY where Y is the national income (GDP), C is consumption, Io and Go are investment and government expenditures that these two variables are exogenously given (i.e. they are some given constants). On the other hand, C is determined by the second equation so it's an endogenous variable. Similarly, total taxes collected in the economy (T) is also endogenously determined. a) What is the economic interpretation of the parameters a and t? b) Express this model in matrix form. As we saw in class, there are different ways to put the system into a matrix form. I ask you to form in two different ways: obtain a matrix form in which the vector of unknowns contains the vari- ables Y, C, T. obtain a matrix form in which the vector of unknowns contains only the variables Y and C. Find the values of the endogenous variables by matrix inversion. For this part suppose Io = 31, Go = 20, a = 0.9, and t = 0.2. d) Now assume that the nation maintains a balanced budget, that is, the govern- ment spending is exactly equal to the total tax revenues. Express this model in matrix form.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 6 images

Blurred answer
Knowledge Booster
Aggregate Expenditure Schedule
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Economics:
Economics:
Economics
ISBN:
9781285859460
Author:
BOYES, William
Publisher:
Cengage Learning