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Economics Dynamics Problems 157

Economics Dynamics Problems 157 - values for all n which...

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Discrete dynamic systems 141 19. Show that neither Mathematica nor Maple can solve the following dif- ference equation x t + 1 = x t 1 + x t Use either programme to generate the first elements of the series up to t = 10, and hence show that this indicates a solution. 20. A Fibonacci series takes the form x n = x n 1 + x n 2 x 0 = 1 and x 1 = 1 (i) Use a spreadsheet to generate this series, and hence show that the series is composed of integers. (ii) Solve the recursive equation with a software package and show that all of its factors are irrational numbers but that it takes on integer values for all
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Unformatted text preview: values for all n , which are identical to those in the spreadsheet. Additional reading ±or additional material on the contents of this chapter the reader can consult Allen (1965), Baumol (1959), Baumol and Wolff (1991), Chiang (1984), Domar (1944), Elaydi (1996), ±armer (1999), Gapinski (1982), Goldberg (1961), GrifFths and Oldknow (1993), Hicks (1950), Holmgren (1994), Jeffrey (1990), Kelley and Peterson (2001), Samuelson (1939), Sandefur (1990), Shone (2001), Solow (1956) and Tu (1994)....
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