Consider a consumer whose preferences are represented by the perfect substitutes utility function U (x, y) = 2x + y. The consumer has an income of I = 60 and the prices of the two goods he cares about are given by px =1and py =2.
(a) Write down the consumerâs utility maximization problem.
(b) Draw budget constraint and representative indiâµerence curves on the same graph.
(c) Find the consumerâs optimal consumption bundle, (x*, y*), and depict the situation on a graph.
(d) What is the share of income spent on good x? Explain briefly why this makes sense for this consumer
given the above prices.
(e) Suppose the price of good x is fixed at 1, but that the price of good y starts to fall from 2. Find that
value of , call it py* , for which the following statement is true: If the price of good y falls below py* , the
consumerâs demand for good x becomes zero.
Consider a consumer whose preferences are represented by the perfect substitutes utility function U (x, y) = 2x + y. The consumer has an income of I = 60 and the prices of the two goods he cares about are given by px =1and py =2.
(a) Write down the consumerâs utility maximization problem.
(b) Draw budget constraint and representative indiâµerence curves on the same graph.
(c) Find the consumerâs optimal consumption bundle, (x*, y*), and depict the situation on a graph.
(d) What is the share of income spent on good x? Explain briefly why this makes sense for this consumer
given the above prices.
(e) Suppose the price of good x is fixed at 1, but that the price of good y starts to fall from 2. Find that
value of , call it py* , for which the following statement is true: If the price of good y falls below py* , the
consumerâs demand for good x becomes zero.
