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Is this a case for Lambert?

  1. Dec 14, 2012 #1
    Dear Forum,

    I am a researcher in the field of microeconomics and I came across this equation which I would like to solve for [itex]k[/itex]. It looks a little bit like the Lambert function. But I am stuck here.
    [itex]\Omega = \rho^k (1-k\cdot \ln \rho) [/itex]

    Do you have an idea how I could proceed?

    Kind regards,
    Samuel
     
  2. jcsd
  3. Dec 14, 2012 #2
    Yes, it is !
     

    Attached Files:

  4. Dec 14, 2012 #3
    Jacquelin gave the answer... but I'm interested, how did this come up?
     
  5. Dec 20, 2012 #4
    Thank you Jacqueline!!

    This is from a model where the demand of a consumer accumulates if he does not make a purchase in one period. This accumulated deteriorates with a factor ρ (e.g.0.9). After k periods without purchase, the demand is [itex]\rho + \rho^2 + ... + \rho^k = \frac{1-\rho^k}{1-\rho}[/itex].

    The term shown in my problem is from a firm's FOC who chooses a set of prices for high-valuation consumers (who purchase in each period) and low-valuation purchases (whose demand accumulates).

    Best,
    Samuel
     
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