In Cambridge, there are individuals from three different citizenships: Ethiopians, Brazilians, and Americans. Coffee is only sourced from Brazil and Ethiopia. Brazilians and Ethiopians only like to drink coffee from their own country, while for Americans a cup of coffee is the same regardless from its origin (Brazil or Ethiopia). All of them have the same level of income denoted byIandis some coefficient greater than0.

(1) What is a utility function for Americans?

(2) What is the magnitude (i.e. the absolute value) of the marginal rate of substitution for Americans? (Suppose Brazilian coffee is on they-axis.)

(3) What is a utility function for Brazilians?

(4) What is the magnitude (i.e. the absolute value) of the marginal rate of substitution for Brazilians? (Suppose Brazilian coffee is on they-axis.)

(5) What is a utility function for Ethiopians?

Continuing with the above coffee example,

(6) ifP_b < P_e, what is the optimal consumption bundle for Americans?

(7) IfP_b < P_e, what is the optimal consumption bundle for Brazilians?

(8) IfP_b < P_e, what is the optimal consumption bundle for Ethiopians?