Consider an economy in which there are two consumers (i {A, B}) and two commodities (1 {1, 2}). Both consumers have preferences that de- fined over bundles of non-negative amounts of each of the two commodities. Consumer A's preferences can be represented by the utility function U4 = (21,14) = min (11,2). Consumer B's preferences can be represented by the utility function UB = (, ) = min (2) Suppose that consumer A is endowed with an income of y4 > 0, and consumer B is endowed with an income of y4 > 0. This means that the aggregate amount of income in this economy is y = y4 +yB > 0. Both consumers face a common price vector p = (P1, P2)", where p, is the strictly positive and finite price of commodity one, and p2 is the strictly positive and finite price of commodity two. 1. Find consumer A's ordinary demand functions for both commodity one and commodity two, and then use these to find consumer A's indirect utility function. 3 2. Find consumer B's ordinary demand functions for both commodity one and commodity two, and then use these to find consumer B's indirect utility function. 3. Use your answers to part (1) and part (2) of this question to find the aggregate ordinary demand functions for both commodity one and commodity two. 4. Do the aggre demand functions that you found in part (3) of this question depend on the entire distribution of income in the economy, or only on the aggregate amount of income in the economy? 5. Discuss the relationship between your answer to part (4) of this ques- tion and the indirect utility functions for consumer A and consumer B. Consider an economy in which there are two consumers (i {A, B}) and two commodities (1 {1, 2}). Both consumers have preferences that de- fined over bundles of non-negative amounts of each of the two commodities. Consumer A's preferences can be represented by the utility function U4 = (21,14) = min (11,2). Consumer B's preferences can be represented by the utility function UB = (, ) = min (2) Suppose that consumer A is endowed with an income of y4 > 0, and consumer B is endowed with an income of y4 > 0. This means that the aggregate amount of income in this economy is y = y4 +yB > 0. Both consumers face a common price vector p = (P1, P2)", where p, is the strictly positive and finite price of commodity one, and p2 is the strictly positive and finite price of commodity two. 1. Find consumer A's ordinary demand functions for both commodity one and commodity two, and then use these to find consumer A's indirect utility function. 3 2. Find consumer B's ordinary demand functions for both commodity one and commodity two, and then use these to find consumer B's indirect utility function. 3. Use your answers to part (1) and part (2) of this question to find the aggregate ordinary demand functions for both commodity one and commodity two. 4. Do the aggre demand functions that you found in part (3) of this question depend on the entire distribution of income in the economy, or only on the aggregate amount of income in the economy? 5. Discuss the relationship between your answer to part (4) of this ques- tion and the indirect utility functions for consumer A and consumer B
