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Is this a case for Lambert? 
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#1
Dec1412, 05:01 AM

P: 4

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 (1k\cdot \ln \rho) [/itex] Do you have an idea how I could proceed? Kind regards, Samuel 


#2
Dec1412, 03:18 PM

P: 759

Yes, it is !



#3
Dec1412, 08:47 PM

P: 242




#4
Dec2012, 01:37 AM

P: 4

Is this a case for Lambert?
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 highvaluation consumers (who purchase in each period) and lowvaluation purchases (whose demand accumulates). Best, Samuel 


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