In: Economics
1. Stephanie is planning an office party. She has the following utility function for fruit and cheese:
U ( F , C ) = min { 6 F , 2 C } |
She has an income equal to $ 50 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 $ 1 and the price of cheese
per pound equals $ 3 .
During the second week of October the price of fruit increased to $
5 . 25 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.
2. Stephanie is planning an office party. She has the following utility function for fruit and cheese:
U ( F , C ) = min { 2 F , 2 C } |
She has an income equal to $ 50 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 $ 1 and the price of cheese
per pound equals $ 2 .
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 income effect of this price
change measured in pounds of fruit? Round your answer to the fourth
decimal point.
1) These goods are perfect complements which are always consumed
together in the fixed proportion.
So, 6F = 2C
So, C = 6F/2 = 3F
So, C = 3F
Budget constraint: Pf*F + Pc*C = Income(M)
So, Pf*F + Pc(3F) = M
So, F(Pf + 3Pc) = M
So, F = M/(Pf + 3Pc)
So, F = 50/(1 + 3*3) = 50/10 = 5
Substitution effect: Change in M = (Pf' - Pf)F = (5.25 - 1)*5 =
4.25*5 = 21.25
New income, M' = M +Change in M = 50 + 21.25 = 71.25
F' = M'/(Pf' + 3Pc) = 71.25/(5.25 + 3*3) = 71.25 /(5.25+9) =
71.25/14.25 = 5
So, substitution effect on F = F' - F = 5 - 5 = 0
SE = 0
2. These goods are perfect complements which are always consumed
together in the fixed proportion.
So, 2F = 2C
So, C = F
Budget constraint: Pf*F + Pc*C = Income(M)
So, Pf*F + Pc(F) = M
So, F(Pf + Pc) = M
So, F = M/(Pf + Pc)
F = 50/(2+2) = 50/4 = 12.5
Substitution effect is zero for complementary goods.
At Pf' = 6; F' = 50/(6+2) = 50/8 = 6.25
Income effect on F = F' - F = 6.25 - 12.5 = 6.25
So, IE = 6.25