EC 3040 - Consider a consumer who consumes only two goods

1. Consider a consumer who consumes only two goods, xand y. His utility over these two goods is given by U(x, y) = xy. The budget constraint of the consumer is given by 3x+ 9y= 216, where 3 is the price of good x, 9 is the price of good y, and 216 is the total income of the consumer.

(a) Find the optimal quantities of good xand ythat the consumer is going to consume. Show the solution in a graph. What level of utility is the consumer going to achieve with this bundle?

(b) Now assume that the price of good xincreases to 6. Find the new optimal consumption bundle and show it in a graph.

(c) Find the income and substitution effects associated with the increase in the price of x. Show your result in a graph.

(d) Given your result in (c), what type of goods are xand y(normal, inferior, or Giffen)?