Unformatted text preview: G for all t E t = C t + I t + G t Y t = E t which on straight substitution gives rise to the secondorder nonhomogeneous recursive equation Y t − ( b + v ) Y t − 1 + vY t − 2 = a + G The particular solution is found by letting Y t = Y ∗ for all t . Hence Y ∗ − ( b + v ) Y ∗ + vY ∗ = a + G i.e. Y ∗ = a + G 1 − b In other words, in equilibrium, income equals the simple multiplier result. The complementary result, Y c , is obtained by solving the homogeneous component Y t − ( b + v ) Y t − 1 + vY t − 2 = which has the characteristic equation x 2 − ( b + v ) x + v = with solutions r , s = ( b + v ) ± ± ( b + v ) 2 − 4 v 2 11 Samuelson originally related investment to lagged consumption rather than lagged income....
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 Fall '11
 Dr.Gwartney
 Economics, Macroeconomics, Equals sign, Yt, Samuelson, Logistic map, DISCRETE DYNAMIC SYSTEMS

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