ECON475ps2 - Middle East Technical University Department of...

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Middle East Technical University Department of Economics ECON 475-Introduction to Mathematical Economics Fall 2009-2010 Problem Set 2 Ebru Voyvoda and Ozlem Tonguc 1. Suppose at time t=0, you borrow 100,000 TL at a fixed interest rate i = 5% per year. You are supoosed to repayy your debt in 20 equal repayments, so that after n =20 years, your debt drops down to zero. What will be the amount of each repayment. Explain. 2. For each of the difference equations below: (i) 28 75 . 0 1 + - = - t t x x (ii) 1 75 . 0 - - = t t x x (iii) 28 5 . 7 1 - - = - t t x x (iv) 28 5 . 7 1 + = - t t x x a. Explain whether the each of the systems in (i)-(iv) is globally asymptotically stable. b. For each of the stable stems in (i)-(iv) compute the steady state. c. For each of the difference equations (i)-(iv), suppose x 0 = 10. Write down expressions for x 1 , x 2 , x 5 . d. For each of the difference equations (i)-(iv), draw how x t changes through time. Comment. e. Now, try drawing the phase diagram for each of the difference equations.
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