A two sector lagged-income model is defined by Y t = C t + I t C t = 0.8Y t-1 + 200 I t = 1000 where Y t , C t and I t denote national income, consumption

A two sector lagged-income model is defined by

Yt = Ct + It
Ct = 0.8Yt-1 + 200
It  = 1000
where Yt, Ct and It denote national income, consumption and planned investment in time period t. The initial value of national income is Y0 = 5000.
(a) Use these relations to work out Y2 and C2.
(b) Derive a first-order difference equation relating Yt and Yt-1.
(c) Solve the difference equation to express Yt in terms of t.
(d) Verify that your general formula in part (c) agrees with the value of Y2 calculated in part (a).
(e) Find an expression for Ct in terms of t and hence determine the time period in which the consumption first exceeds 4750.

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Question Details
Chapter # 9
Section: Examination questions
Problem: 4
Posted Date: April 18, 2019 10:26:23