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 w = PN N + PAT where w is the nominal wage, Pn the price of nontradables, and PT the price of tradables. a) Solve for the relative price of nontradables to tradables in terms of Ar, N, and a. How does shifts in a affect relative prices? Does an increase in AT generate a real appreciation (assuming Pr is the same across countries in a common currency, and so the real exchange rate is driven by movements in PT b) Now suppose the government taxes workers t amount (so disposable income is w-t. The government spends everything on nontraded goods. How does this affect the real exchange rate? c) Now suppose the country must pay X units of tradables (per capita) to a foreign country to repay a debt. Domestic consumption of tradables is therefore At - X. How does this affect the real exchange rate? 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 w = PN N + PAT where w is the nominal wage, Pn the price of nontradables, and PT the price of tradables. a) Solve for the relative price of nontradables to tradables in terms of Ar, N, and a. How does shifts in a affect relative prices? Does an increase in AT generate a real appreciation (assuming Pr is the same across countries in a common currency, and so the real exchange rate is driven by movements in PT b) Now suppose the government taxes workers t amount (so disposable income is w-t. The government spends everything on nontraded goods. How does this affect the real exchange rate? c) Now suppose the country must pay X units of tradables (per capita) to a foreign country to repay a debt. Domestic consumption of tradables is therefore At - X. How does this affect the real exchange rate