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Consider the Keynesian consumption function Yt=B₁ + B₂x2+ + Et ( where y, is per capita consumption, and x2+ is per capita income. The coefficient ₂ is interpreted causally as the marginal propensity to consume, and we expect 0 < $₂ < 1. At the same time, X2t=yt + Z2t where Z2, denotes per capita investment. Assume for now that investment is exogenous and Cov(&₂, 22t) = E[+22+] = 0 Darike the: show steps reduced form (

Consider the Keynesian consumption function Yt=B₁ + B₂x2+ + Et ( where y, is per capita consumption, and x2+ is per capita income. The coefficient ₂ is interpreted causally as the marginal propensity to consume, and we expect 0 < $₂ < 1. At the same time, X2t=yt + Z2t where Z2, denotes per capita investment. Assume for now that investment is exogenous and Cov(&₂, 22t) = E[+22+] = 0 Darike the: show steps reduced form (

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider the Keynesian consumption function Yt =B₁ + B₂x2+ + Et ( where y, is per capita consumption, and x2+ is per capita income. The coefficient ₂ is interpreted causally as the marginal propensity to consume, and we expect 0 < ₂ < 1. At the same time, X2t = Yt + Z2t where Z2, denotes per capita investment. Assume for now that investment is exogenous and Cov(Et, 22t) = E[EtZ2+] = 0 Darixe, the: show steps reduced form X2t Yt = = B₁ 1- B₂ B₁ 1-₂ + + 1 1-₂ B₂ 1-₂ -Z2t + -Z2t + ( 1 1- B₂ 1 1-₂ -Et -Et
Transcribed Image Text:Consider the Keynesian consumption function Yt =B₁ + B₂x2+ + Et ( where y, is per capita consumption, and x2+ is per capita income. The coefficient ₂ is interpreted causally as the marginal propensity to consume, and we expect 0 < ₂ < 1. At the same time, X2t = Yt + Z2t where Z2, denotes per capita investment. Assume for now that investment is exogenous and Cov(Et, 22t) = E[EtZ2+] = 0 Darixe, the: show steps reduced form X2t Yt = = B₁ 1- B₂ B₁ 1-₂ + + 1 1-₂ B₂ 1-₂ -Z2t + -Z2t + ( 1 1- B₂ 1 1-₂ -Et -Et
Expert Solution
Step 1

Given 

Keynsian consumption function 

yt=β1+β2x2t+εt                                 ...... (1)

At the same time x2t=yt+z2t             ....... (2)

We have to find the reduced form equation.

To find reduced form equation, we substitute value from equation 2 into equation 1

 

steps

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