1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Feb 11, 2014 #1


    User Avatar

    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!
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted