Economics Dynamics Problems 216

Economics Dynamics - 01 and a = 4 b = 2 and c = 4 Plot the system for initial point x y z =(0 1 1 1 in(i x y-plane(ii x z-plane(iii y z-plane

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200 Economic Dynamics 12. Consider the following Walrasian price and quantity adjustment model φ ± ( Y ) = 0 . 5 + 0 . 25 Y D ( p ) =− 0 . 025 p 3 + 0 . 75 p 2 6 p + 40 ˙ p = 0 . 75[ D ( p ( Y )) Y ] ˙ Y = 2[ p φ ± ( Y )] (i) What is the economically meaningful Fxed point of this system? (ii) Does this system have a stable limit cycle? 13. Reconsider the system in question 12, but let the quantity adjustment equation be given by ˙ Y = β [ p φ ± ( Y )] Let β = 2 , 2 . 5 , 3 and 3 . 2. What do you conclude about the long-run be- haviour of this system? 14. Consider the following system φ ± ( Y ) = 0 . 5 + 0 . 25 Y D ( p ) =− 0 . 025 p 3 + 0 . 75 p 2 6 p + 40 ˙ p = α [ D ( p ( Y )) Y ] ˙ Y = 2[ p φ ± ( Y )] Let α = 0 . 5 , 0 . 75 and 1. What do you conclude about the long-run be- haviour of this system? 15. Set up the R¨ossler attractor ˙ x =− y z ˙ y = x + ay ˙ z = b + z ( x c ) on a spreadsheet with step size ± t = 0 .
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Unformatted text preview: 01 and a = . 4 , b = 2 and c = 4. Plot the system for initial point ( x , y , z ) = (0 . 1 , . 1 , . 1) in (i) ( x , y )-plane (ii) ( x , z )-plane (iii) ( y , z )-plane Additional reading Additional material on the contents of this chapter can be obtained from Arrow-smith and Place (1992), Beavis and Dobbs (1990), Borrelli et al. (1992), Boyce and DiPrima (1997), Braun (1983), Chiang (1984), ┬▒laschel et al. (1997), Giordano and Weir (1991), Jeffrey (1990), Lynch (2001), Mas-Colell (1986), Percival and Richards (1982), Schwalbe and Wagon (1996), Shone (2001) and Tu (1994)....
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

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