Econ 300 Section 1

Take-home Homework 3

28 Points

Due Date: Friday, February 22nd, 2013 by 4pm

Instructions: You can turn your homework in during class or into the economics department where they will time stamp your homework and place it in my mailbox. Make sure you show your work.

  1. (4 points) What information is contained in the slope of an indifference curve? Why are these curves typically convex to the origin? (minimum of 4 sentences)
  1. Andy purchases only two goods, apples () and kumquats (). He has income of $400 and can buy apples at $10 per pound and kumquats at $8 per pound. His utility function is
  1. (4 points) What bundle of apples and kumquats should he purchase to maximize his utility?
  2. (4 points) Graph Andy’s utility maximizing bundle, making to graph his indifference curve and his budget constraint. Label axis.
  1. Vasco’s utility function is

The price of is , the price of is , and his income is

  1. (4 points) What is his optimal bundle (utility maximizing bundle)?
  2. (4 points) Graph Vasco’s utility maximizing bundle, making sure to graph his indifference curve and his budget constraint. Label axis.
  1. (4 points) Confirm that if a consumer’s utility function is described by

where the , , and prices are and , there is no unique utility-maximizing solution regardless of income level. What does this tell you about X and Z as commodities? (Hint: draw a graph showing a budget constraint and indifference curve using the information provided.)

  1. (4 points) Suppose Carmela’s income is $100 per week, which she allocates between sandwiches and books. Sandwiches cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to $5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Carmela might have more than one utility-maximizing solution?