3. In the Balassa-Samuelson model we covered in class, demand played no role in determining the relative price of tradables and non-tradables. This was because each sector had "constant returns to scale," or, in this case, production was linear in labor inputs. Any demand shift between sectors would be accommodated by moving labor across sectors, but leaving marginal cost unchanged. In this question, we drop that assumption. In particular, suppose the nontraded good is in fixed supply (like land). Each period, N units (per capita) are produced, regardless of prices or demand. The tradable sector is as in class, with one unit of labor producing AT units of tradable output. Suppose that demand is such that a fraction a of disposable income is spent on N and a fraction 1-a is spent on tradables. Total income (per capita) is given by