100A:
Intermediate Microeconomics, Dr. Famulari, Problem Set #3
Question 1:
Matt gets utility from candy bars (C) and movies (M).
Matt ALWAYS eats 2 candy
bars at each movie he attends.
Extra candy without seeing another movie is of no value to
Matt, just as going to the movies is of no value without the candy bars.
Matt maximizes his
utility from movies and candy bars subject to a budget constraint.
1A.
What type of utility function represents Matt’s preferences?
Write down an expression
for Matt’s utility.
1B.
Illustrate the consumer’s problem graphically.
Be sure to CAREFULLY indicate what
you know and what you will be solving for in this problem.
1C.
Will you be able to use the Lagrange multiplier technique to solve for Matt’s utility
maximizing combinations of movies and candy bars?
Why or why not?
1D.
Solve for Matt’s utility maximizing combination of movies and candy bars as a function
of prices and income.
Note:
M*(P
M
, P
C
, I) and C*(P
M
, P
C
, I) are the ordinary (or
uncompensated) demand functions.
1E.
What is Matt’s maximum utility, U(M*(P
M
, P
C
, I), C*(P
M
, P
C
,I))?
Note that maximum
utility is
indirectly
a function of prices and income.
Thus we call
V(P
M
, P
C
, I)= U(M*(P
M
, P
C
, I), C*(P
M
, P
C
,I)), the indirect utility function.
1F.
You have solved for general expressions for C*, M* and V.
Now, suppose the price of
movies is $4, the price of candy bars is $2, and the consumer’s income is $24.
What are
the numerical values of C*, M* and U*?
Put these values on your graph.
Question 2: