# Is this a case for Lambert?

by Sammuueel
Tags: case, lambert
 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 $k$. It looks a little bit like the Lambert function. But I am stuck here. $\Omega = \rho^k (1-k\cdot \ln \rho)$ Do you have an idea how I could proceed? Kind regards, Samuel
 Quote by Sammuueel Dear Forum, I am a researcher in the field of microeconomics and I came across this equation which I would like to solve for $k$. It looks a little bit like the Lambert function. But I am stuck here. $\Omega = \rho^k (1-k\cdot \ln \rho)$ Do you have an idea how I could proceed? Kind regards, Samuel
 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 $\rho + \rho^2 + ... + \rho^k = \frac{1-\rho^k}{1-\rho}$. 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