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Bob,
This is the way labour markets work: v(s, y, λ) max{λ, R(s, y) min[ λ, β ∫ v(s′, y, λ) f(s′, s)ds′]}.
Ed
Robert Lucas went on to explain in his professional memoir about this exchange in the early 1970s that:
we had agreed on notation: s stood for the state of product demand at a particular location, y stood for the number of workers who were already at that location, R(s, y) was the marginal product of labour implied by these two numbers, and v(s, y) stood for the present value of earnings that one of these workers could obtain if he made his decision whether to stay at this location or leave optimally.
Other features of the equation were as novel to me as they are (I imagine) to you…
a single parameter—Ed’s λ—stood for two different things: the present value of earnings that all searching workers would have to expect in order to leave a location and the present value that a particular location would need to offer to receive new arrivals…
If I had to pick a single day to represent what I like about a life of research, it would be this one.
Ed’s note captures exactly why I think we value mathematical modelling: it is a method to help us get to new levels of understanding the ways things work.
Utopia, you are standing in it! 
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