Question

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

U ( F , C ) = min { 8 F , 8 C }

She has an income equal to $ 100 to spend on cheese and fruit. She prices the fruit and cheese during the first week of October. At this time the price of fruit per pound $ 5 and the price of cheese per pound equals $ 4 .

During the second week of October the price of fruit increased to $ 6 per pound. If Stephanie purchases the fruit and cheese at this time what is the magnitude of the substitution effect of this price change measured in pounds of fruit? Round your answer to the fourth decimal point.

Answer 1

Pf=price of fruit

Pc=prise of cheese

1) These goods are perfect complements which are always consumed together in the fixed proportion.
8F =8C
C = 8F/8 = F
C = F

Budget constraint: Pf*F + Pc*C = Income(M)
Pf*F + Pc(F) = M
F(Pf + Pc) = M
F = M/(Pf + 2Pc)

F = 100/(5 + 2*4) = 7.69

Substitution effect: Change in M = (Pf' - Pf)F = (6 - 5)*7.69 = 7.69
New income, M' = M +Change in M = 100 + 7.69 = 107.69
F' = M'/(Pf' + 2Pc) = 107.69/(6 + 2*4) = 7.69

So, substitution effect on F = F' - F = 7.69-7.69 = 0