hw8a - ECON475 HW#8 Answers = = 1 1 1 = Steady-state value...

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Unformatted text preview: ECON475 HW #8 Answers = = 1. + - 1- + 1- = Steady-state value For the following cases, draw diagrams. Best way to do is giving values and looking at what happens, then analyzing mathematically. a. -, -1 , - lim < Thus there is no converge to the steady state. b. 0, 1 , < lim - = - when t is even. = when t is odd. lim - Thus, c. Thus there is no converge to the steady state. d. < -1, > > 1, Under the conditions given above, lim approaches to = as . 1- =0 - =. Thus there is no converge to the steady state. e. lim = 1, - - = lim lim > - - = when t is even. = - when t is odd. + = = . 1- 1- 1- The system is at its the steady state. = -1, < =0 f. Case I: = -1 - 1- + 1- 2 = 1- , - , - , , Case II: > 2 - , = , = 2 , given 2 < - ,2 - > . , < In both cases, the system does not converge to the steady state value. 2. Consider the following demand and supply functions: - = 2 = - Then, Also, a. If = = + = + and =- - = + . - <2 , then | | < 1. = and lim = Thus the price converges to b. If > 2 Assume , then | | > 1. < . Then, lim , regardless of the initial price. =0 - - = = Assume > - - . Then, lim Thus the price diverges from to c. If =2 , then | | = 1. < > , unless = 2 = - . Case I: Case II: lim thus, 2 - thus, 2 - + - > . The prices oscillate between < . The prices oscillate between and . and . In conclusion, if supply is more elastic than the demand, the equilibrium is not stable. ...
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