Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter10: Keynesian Macroeconomics And Economic Instability: A Critique Of The Self Regulating Economy
Section: Chapter Questions
Problem 7QP
Related questions
Question
![Consider the Keynesian consumption function
Yt =B₁ + B₂x2t + εt
(
where yt is per capita consumption, and x2+ is per capita income.
The coefficient B₂ is interpreted causally as the marginal propensity
to consume, and we expect 0<B₂ < 1.
At the same time,
X2t = Yt + Z2t
where z2t denotes per capita investment.
Assume for now that investment is exogenous and
Cov(&t, Z2t) = E[EtZ2t] = 0
Darive/ show that the coverance is this:
Cov(x2t, Et)
o² = Var(&t)
=
1
1- B₂
02
1- B₂
(
1
1- B₂ Var (2₂)
-Cov(Z2t, &t) +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc93dd3a-e660-4464-bc8c-e382a2c34aae%2Ff1103d49-53cb-41a3-a6b3-e0fc8733038b%2Fm96k4ur_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the Keynesian consumption function
Yt =B₁ + B₂x2t + εt
(
where yt is per capita consumption, and x2+ is per capita income.
The coefficient B₂ is interpreted causally as the marginal propensity
to consume, and we expect 0<B₂ < 1.
At the same time,
X2t = Yt + Z2t
where z2t denotes per capita investment.
Assume for now that investment is exogenous and
Cov(&t, Z2t) = E[EtZ2t] = 0
Darive/ show that the coverance is this:
Cov(x2t, Et)
o² = Var(&t)
=
1
1- B₂
02
1- B₂
(
1
1- B₂ Var (2₂)
-Cov(Z2t, &t) +
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 14 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
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.Recommended textbooks for you
![Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337617383/9781337617383_smallCoverImage.gif)
Economics (MindTap Course List)
Economics
ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning
![Macroeconomics](https://www.bartleby.com/isbn_cover_images/9781337617390/9781337617390_smallCoverImage.gif)
![MACROECONOMICS FOR TODAY](https://www.bartleby.com/isbn_cover_images/9781337613057/9781337613057_smallCoverImage.gif)
![Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337617383/9781337617383_smallCoverImage.gif)
Economics (MindTap Course List)
Economics
ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning
![Macroeconomics](https://www.bartleby.com/isbn_cover_images/9781337617390/9781337617390_smallCoverImage.gif)
![MACROECONOMICS FOR TODAY](https://www.bartleby.com/isbn_cover_images/9781337613057/9781337613057_smallCoverImage.gif)
![Economics For Today](https://www.bartleby.com/isbn_cover_images/9781337613040/9781337613040_smallCoverImage.gif)
![Economics:](https://www.bartleby.com/isbn_cover_images/9781285859460/9781285859460_smallCoverImage.gif)
![Exploring Economics](https://www.bartleby.com/isbn_cover_images/9781544336329/9781544336329_smallCoverImage.jpg)
Exploring Economics
Economics
ISBN:
9781544336329
Author:
Robert L. Sexton
Publisher:
SAGE Publications, Inc