Carina buys two goods, food F and clothing C, with the utility function U = FC+ F. Her marginal utility of food is MUF= C + 1 and her marginal utility of clothing is MUC= F. She has an income of 20. The price of clothing is 4.
a) Derive the equation representing Carinas demand for food, and draw this demand curve for prices of food ranging between 1 and 6.
b) Calculate the income and substitution effects on Carinas consumption of food when the price of food rises from 1 to 4, and draw a graph illustrating these effects. Your graph need not be exactly to scale, but it should be consistent with the data.
c) Determine the numerical size of the compensating variation (in monetary terms) associated with the increase in the price of food from 1 to 4.
Given- U=FC+ F MUF = C+1, MUC= F M=20 (Income) PC =4 a) PF ranges from 1 to 6 MRS= MUc/MUF= F/C+1 The budget line- 4C+PfF=20 Slope = 4/PF For deriving demand curve, MRS= PC/PF For P=1: => F/C+1 = 4/ PF => C= (PFF-4)/4 Putting the value in budget line, we get, => 4(PFF-4)/4 +PfF=20 =>2 PfF-4=20 => PfF=24/2 => F=12/ Pf The demand for food is given by 12/ Pf b) Price of food rises from 1 to 4 Demand when P=1: F1=12; C=2 Demand when P=4: F2=3; C=2 Total price effect on food = 3-12 =-9 For substitution effect, M-M=F1*(P2-P1) => M-M= 12*3 =>M= 36+20 =>M= 56 Using the same process as in a) we calculate demand of food at new price 4 and new income which is 56. We get F=7.5, C= 6.5 So , substitution effect= (demand of F at P=4 and M=56)- (demand of F at P=1 and M=20) = 7.5-12 =…
.5 Income effect= (demand of F at P=4 and M=20)- (demand of F at P=4 and M=56) = 3- 7.5 = -4.5 Price effect= substitution effect + income effect c) Compensating Variation is the change in income level to keep the consumer on same utility level. Utility with P=1, U= 12*2+2 =26 We want utility with P=4 to be 26, we put the demand of F in utility function We derive it in same way as in part a) with income= M We get, => 26= 2*(M+4)/2PF+(M+4)/2PF => M= 65.33 PF=4 So, Compensating Variation= M-M = 65.33-20 =45.33