This is a question about one single step of a solution of a long equation.
where P, U and V are variables. a, b, c, d are constants and t is the time, which are measured in discrete periods.
The question is how to go from equation 1 to equation 3, and how the L appears.
I have solved it until equation 2, and I see that the solution requires the extraction of P out of the bracket on the left hand side. Problem becomes how to do it, since the P minus one period doesn't equal P of current period. Nevertheless the key somehow does this. Does this require some other method than simple algebra?
The key mentions it is a "stochastic difference equation".