Generalize the two-country model of a floating exchange rate to take account of the distinction between traded and non-traded goods. Assume that the price index in each country is
Where PT, PN are the prices of the two goods in the domestic country, and stars denote the foreign country as usual. PPP applies only to trade goods, since non-traded good, prices are determined in the domestic economy.
a) Derive the equation for exchange rate in term of relative money stocks, income and non traded goods prices.
b) By log differentiation, describe the effect of changes in the exogenous variables and also the part played by the index weights, α, 1- α.