Quiz 3

Q:
Kathy enjoys roses (r) and chocolate (c).
Her utility is given by u(r,c) = rc.
Her husband is going to spend $40 on her for Valentine’s.
A month before the holiday the market prices are Pr=1 and Pc=2; however,
on Valentine’s day the price of roses has risen to Pr=4.
What is the total effect of this price change on the quantity he will
decide to purchase?

A:
To find the total effect, we must find the starting bundle and the ending
bundle.

To find the starting bundle: Note
that this is a Cobb-Douglas utility so the two equations are MRS=Pr/Pc and the
initial B.C.. For this problem
these equations are c/r=2/1 and 40=1r+2c. Solving
these 2 equations yields r_{s}=20 and c_{s}=10.

To find the final
bundle: Now the 2 equations are MRS=Pr/Pc
and the final B.C.. For this
problem these equations are c/r=2/1 and 40=4r+2c.
Solving these 2 equations yields r_{f}=5 and c_{f}=10.

Now
that we know r_{s} and r_{f} we can answer the question.
The total effect is r_{s}-r_{f}=20-5=15.
Notice that we refer to the Total Effect as well as the Income and
Substitution effects in terms of the good that experienced the price change.