Intermediate Microeconomics
Problem Set 1
Part 1: The Basic Consumer Problem
All there is are movies (m) and food (f). The price of movies is $10 while the price of food is $5. I have $145 to spend on these two goods. My preferences are described by the following utility function:
??(??, ??) = ?? + ?? + ????
1. Write down my budget constraint.
2. Solve for my optimal bundle of movies and food.
3. What is my level of utility at this bundle?
4. Graph the budget constraint and indifference curve for the optimal bundle.
Part 2: A Tax
Continuing from Part 1
In order to raise revenues, the city government has imposed a $2 quantity tax on movies, and $1 quantity tax on food. Coincidentally, I have gotten a $5 raise, meaning that I now have $150 to spend.
5. Write down my new budget constraint.
6. Solve for my new optimal bundle of movies and food.
7. What is my new level of utility at this bundle? Am I better or worse off?
8. Graph the budget constraint and indifference curve for the new optimal bundle on a separate graph.
9. How much revenue is the city government raising from my economic activity?
10. How much would I be willing to pay the city government to get rid of these taxes? In other words, what value of a lump-sum tax would leave me just as well off as this tax?
Part 3: Deeper Analysis
Continuing from Part 1 (That means ignore everything in part 2)
The city government is considering a tax on movies to raise additional revenue. They believe that the preferences and income described in part 1 are a good representation of the average citizen. The city is desperate, and wants to get as much revenue as they can.
Using the preferences, prices, and income from part 1, determine the level of quantity tax that will maximize government revenues. Note that government revenues in this case will be ?? ∗ ??, but that the choice of ?? will vary based on ??.