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 rs=20 and cs=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 rf=5 and cf=10.

Now that we know rs and rf we can answer the question.  The total effect is rs-rf=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.