Economics Dynamics Problems 154

Economics Dynamics Problems 154 - t + 6 (iv) y t + 1 = . 5...

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138 Economic Dynamics > solve(eq2=-1,r); 1 6 , 1 + 6 > evalf(%); 1 . 449489743 , 3 . 449489743 > solve(eq2=1,r); 1 , 3 Exercises 1. Classify the following difference equations: (i) y t + 2 = y t + 1 0 . 5 y t + 1 (ii) y t + 2 = 2 y t + 3 (iii) y t + 1 y t y t = 4 (iv) y t + 2 2 y t + 1 + 3 y t = t 2. Suppose you borrow an amount P 0 , the principal, but you repay a Fxed amount, R , each period. ±ormulate the general amount, P t + 1 , owing in period t + 1, with interest payment r %. Solve for P n . 3. In question 2, suppose the repayment is also variable, with amount repaid in period t of R t . Derive the solution P n . 4. Establish whether the following are stable or unstable and which are cyclical. (i) y t + 1 =− 0 . 5 y t + 3 (ii) 2 y t + 1 =− 3 y t + 4 (iii) y t + 1 =− y
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Unformatted text preview: t + 6 (iv) y t + 1 = . 5 y t + 3 (v) 4 y t + 2 + 4 y t + 1 − 2 = 5. Consider y t + 1 = y 3 t − y 2 t + 1 (i) Show that a = 1 is a Fxed point of this system. (ii) Illustrate that a = 1 is a shunt by considering points either side of unity for y . 6. Use a spreadsheet to compare y t + 1 = (1 + a ) y t − by 2 t and y t + 1 = (1 + a ) y t 1 + by t using (i) a = 1.5 b = 0.1 y = 1 (ii) a = 1.5 b = 0.1 y = 22 (iii) a = 2.2 b = 0.1 y = 1 (iv) a = 2.2 b = 0.1 y = 25 (v) a = 1.8 b = 0.15 y = 11.5...
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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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