Question

Sam is planning an office party. He has the following utility function for fruit and cheese:

U ( F , C ) = min { 6 F , 2 C }

He has an income equal to $ 50 to spend on cheese and fruit. He prices the fruit and cheese during the first week of October. At this time the price of fruit per pound $ 1 and the price of cheese per pound equals $ 3 .

During the second week of October the price of fruit increased to $ 5 . 5 per pound. If Sam purchases the fruit and cheese at this time what is the magnitude of the income effect of this price change measured in pounds of fruit? Round your answer to the fourth decimal point.

Answer 1

The utility function U (F,C)= min {6F,2C} is Perfect compliments. The demand function will be:-

F= m/[Pf+ Pc(a/b)] and C= m/[Pf (b/a)+ Pc] where a=6 and b=2

So, F= m/[Pf+ Pc(3)] and C= m/[Pf (3)+ Pc]

The method I am using below is Slutsky as I need to compute income effect for Fruit after price change.