Suppose consumption is modeled by the following:
C = 5,000 + 0.75YP
where YP is permanent income. Suppose also that households estimate their permanent disposable income as a weighted average of disposable income in the current and past two years, according to:
YPt = .6YDt + 0.30YDt-1 + 0.10YDt-2
where YDt is disposable income in this year and the two previous years for YDt-1 and YDt-2, respectively.
A. Suppose that disposable income YD has been equal to $125,000 for three consecutive years (so that YDt = YDt -1 = YDt -2 = $125,000; that is, YD = $125,000 in 2011, 2010, and 2009). What is consumption this year C2011 ?
B. Now suppose that disposable income decreases to $100,000 next year, and then remains at $100,000 in all future years. What is permanent income in next year (YP(2012)) and consumption next year (C2012).
C. What is the level of consumption by the year 2014? Also, what are the short-run (in the first year after the change of YD2012 to $100,000) and long-run marginal propensities to consume (by 2014) after YD has been $100,000 for three years?