3. Consider the following consumption and output functions. Ct = Co+cYt-1 with 0

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3. Consider the following consumption and output functions.
Ct = Co+cYt-1 with 0<c<1
Yt=Ct+It
(1)
(2)
Equation 1 describes the behavior of consumption over time. Consumption at time
t is equal to consumption at time zero plus the marginal propensity to consume
times output at time t - 1. The second equation simply states that output at time t
is equal to consumption at time t plus investment at time t. Assume that It = Io.
1
i. Substitute equation (1) into (2) and solve for the time-path of Yt. Once you
have found the general solution, find the value of the arbitrary constant A.
ii. Find the particular solution assuming that Ct = 200+0.9Yt-1 and Io = 100
and Yo = 4500. Comment on the time-path of Yt.
Transcribed Image Text:3. Consider the following consumption and output functions. Ct = Co+cYt-1 with 0<c<1 Yt=Ct+It (1) (2) Equation 1 describes the behavior of consumption over time. Consumption at time t is equal to consumption at time zero plus the marginal propensity to consume times output at time t - 1. The second equation simply states that output at time t is equal to consumption at time t plus investment at time t. Assume that It = Io. 1 i. Substitute equation (1) into (2) and solve for the time-path of Yt. Once you have found the general solution, find the value of the arbitrary constant A. ii. Find the particular solution assuming that Ct = 200+0.9Yt-1 and Io = 100 and Yo = 4500. Comment on the time-path of Yt.
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