Is this a case for Lambert?


by Sammuueel
Tags: case, lambert
Sammuueel
Sammuueel is offline
#1
Dec14-12, 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 (1-k\cdot \ln \rho) [/itex]

Do you have an idea how I could proceed?

Kind regards,
Samuel
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JJacquelin
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#2
Dec14-12, 03:18 PM
P: 744
Yes, it is !
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piercebeatz
piercebeatz is offline
#3
Dec14-12, 08:47 PM
P: 224
Quote Quote by Sammuueel View Post
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
Jacquelin gave the answer... but I'm interested, how did this come up?

Sammuueel
Sammuueel is offline
#4
Dec20-12, 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 high-valuation consumers (who purchase in each period) and low-valuation purchases (whose demand accumulates).

Best,
Samuel


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