(a) Suppose that households' preferences are Cobb-Douglas over tradable and non-tradable goods: C = C N C 1 T (1) where is the non-tradable weight in consumption. We regard C as both households' utility and aggregate consumption basket. Households with income Y solve the following optimization problem taking Y , PN , and PT as given. max CN ,CT C N C 1 T subject to PN CN + PT CT = Y (2) where PT and PN are the price levels of tradable and non-tradable goods. Express the optimal CN and CT as functions of , Y , PN , and PT .