Econ 111: Intermediate Microeconomics Fall 2007 Homework 2: Budgets and Optimal Choice Due Friday 21st September in class
Jim Campbell jim@brown.edu
Problem 1: A budget set
Steaks (good 1) cost $10 each and hot dogs (good 2) cost $1 each. Jim’s having a cookout and has $50 to spend on food. a) Write down Jim’s budget constraint for food. b) Draw his budget set, making steaks good 1 on the horizontal axis. c) Is the bundle (3, 26) in the budget set? d) What does the slope of the budget line measure? e) What is the opportunity cost of 1 steak? f ) The price of steak falls to $5 each. Draw the new budget constraint. Has the opportunity cost of hot dogs fallen or risen?
Problem 2: An optimal choice
Jim only consumes ice packs and Ace bandages. His income is $60 per week. The price of an ice pack is $10 and the price of an Ace bandage is $5. a) Draw Jim’s budget set, with ice packs on the horizontal axis and Ace bandages on the vertical axis. b) What is the slope of the budget line? c) Jim likes to use an ice pack when he changes his Ace bandage, and won’t use either one separately. Draw three of his indifference curves: the one through point (2,1), the one through (4,4) and the one through (6,8). d) Find a utility function that represents Jim’s preferences. e) What is his optimal choice?
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Problem 3: Price changes
Paco has a utility function U = x1 x2 . He earns income of $100. The price of good 1 is $1 and the price of good 2 is $1. It is possible to consumer non-integer amounts of the goods. a) What is Paco’s optimal choice (hint: Cobb-Douglas utility...)? [Call this choice A] How much utility does he get? b) Draw the budget set and sketch on the same graph the indifference curve that goes through the optimal choice. c) The price of good 1 goes up by 100%. What’s the new p1 ? What is Paco’s new optimal consumption bundle? [Call this choice B] What utility does he get now? d) On the same graph as part b), draw the new budget set, Paco’s new optimal choice, and the indifference curve through it. e) What increase in Paco’s income would be needed to make his original consumption bundle just affordable at the new prices? f ) If we gave Paco the increase in income in e), what would his optimal choice be with this new income and the new prices from c)? [Call it C] g) Remember: the substitution effect is the difference between C and A. Calculate the substitution effect on good 1 using your answers to a) and f). h) Remember: the income effect is the difference between B and C. Calculate the substitution effect on good 1 using your answers to d) and f). i) Is good 1 normal or inferior for Paco?
Extra credit
In class we’ll see a couple of examples of applications of the consumer choice model to real-world issues. Can you think of another example? Talk about the budget set, preferences and optimal choice in your example, and show how the model is affected by a change in parameters, especially by government.
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