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MacroEcon, Stock Prices, Recurrence Relations (and Linear Algebra?)

  1. Feb 11, 2014 #1

    bpr

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    1. The problem statement, all variables and given/known data

    This is a question from an upper level econ course that is giving me quite a bit of trouble. Fluency in linear algebra is assumed for the course. I'm taking a linear algebra course for the first time this semester so I'm still scrambling to learn the basics. If anyone has a good resource to learn linear algebra I would appreciate that as much as any help on this particular problem. So... {subscript} The price of a stock obeys the equations: (1) P{t} = y{t} +β* P{t+1}.
    It is "guessed" that equation (1) implies P{t} = Hx{t} + cλ^t. A, G, H are matrices, c and λ are scalars. β is the discount factor.
    Solve for H, c, and lambda - are they unique?

    2. Relevant equations
    Equations x{t+1} = Ax{t}, y{t} = Gx{t} are also given.

    3. The attempt at a solution
    I found P{t+1} and substituted in the other equations to get: Hx{t} +cλ^t = Gx{t} + β(HAx{t} + cλ^(t+1)) assuming cλ^t = βcλ^(t+1) (therefore beta =1/lambda) H = G(I-βA)^-1
    I'm told this is incorrect but it was my best guess so far.. My next guess would be to put P{t+1} into a geometric series which would solve to a form that looks like cλ^t and then putting the rest into a matrix form. But I feel unfortunately out of my element. Any and all help is greatly appreciated, thank you in advance!
     
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