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Unformatted text preview: ECON475 HW #8 Answers = = 1. +  1 + 1 = Steadystate 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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This note was uploaded on 05/26/2010 for the course ECON 475 taught by Professor Voyvoda during the Spring '10 term at Middle East Technical University.
 Spring '10
 voyvoda
 Economics

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