EXERCISE 9: Utility and demand
J. Wahl – Micro Principles
1. Most people seem to be characterized as having positive but diminishing marginal utility
of income. Graph this, with utility of income on the vertical axis. This observation has
led many people to argue that tax rates should be progressive. Do you agree? Why or
why not?
2. Suppose your income is 100, the price of food is 2, and you only care about food (f).
You know that your utility function is
U = f ½
If you want to maximize your utility, given the budget constraint you have, what amount
of food will you eat? Show your answer graphically.
3. Suppose income and prices are the same as in 2. What amount of food will you eat if
your utility function is U = 50f -f2 ? Show your answer graphically.
4. Suppose your initial endowment is 10 cookies and 6 beers, and your utility is mapped out
by the following indifference curves:
U=100 with bundles of (cookies, beer) of (10,6), (5,7), (4.5,8)
U=130 with bundles of (cookies, beer) of (14,7), (9,8), (8.5,9)
Suppose also that the market price of a beer is 50 cents (small beer) and the market price
of a cookie is $1 (big cookie). Please do the following:
graph the indifference curves and the budget constraint
indicate your endowment point
figure out how many beer and cookies you will end up with, how much utility,
and why
describe generally what “equilibrium” looks like in this sort of model
