Consider the OLG model that we develop in class. There are N people in every generation. Each individual is endowed with y units of goods when young and nothing when old. Suppose that monetary authority prints at money at the rate z but now does not distribute the newly printed money as a lump-sum transfer to the old. Instead, the government distributes the newly printed money by giving each old individual new x dollars for each dollar acquired when young.

Use the government budget constraint to find x as a function of z.