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