Mathematica Problem 1
Use Mathematica to do each of the following:
1. You enjoy both movies, M, and pizza, P. Your utility function for these
two goods is:
U = .6 log M + .4 log P
a. For a given quantity of pizzas, say P = 2, graph your total utility
function for movies. Number of movies should be on the horizontal axis and
total utility on the vertical axis.
b. Suppose the quantity of pizzas increased to 3, show how this would affect
your total utility function.
c. Graph your marginal utility curves for movies and pizza.
d. For total utility equal to 1.27, graph the relationship between M and P
measuring M on the vertical axis and P on the horizontal axis. This curve is
called an indifference curve.
e. Repeat step d for utility levels 1.46 and 1.61, adding your new
indifference curves to your graph from part d. This is called an
indifference map. It is a picture of your preferences.
2. Suppose the price of a pizza is $3 and the price of a movie is $4. You
have $25 per week to spend on pizzas and movies. Therefore, your budget
constraint is:
25 = 3 P + 4 M
a. Graph your budget constraint with M on the vertical axis and P on the
horizontal axis.
b. Suppose your budget for pizzas and movies increases to 30. Add your new
budget constraint to your graph from part a.
c. Repeat step b for a budget of 35.
3. Add the budget constraints from part 2 to your indifference map in part
1. Are there any points of tangency? The points of tangency are called your
income expansion path.
4. Suppose the price of pizza falls to $2. Assume your budget remains at $25
and the price of movies remains at $4 .
a. Graph your old and new budget lines.
b. Add indifference curves for utility levels 1.27 and 1.44. Are there any
points of tangency? The points of tangency are called the price expansion
path. They underlie the demand curve.