Question

Mark has $100 to spend on food (F) and clothing (C). His preferences can be described by the utility function U(F,C) = F0.5C0.5. The price of food is $5, and the price of clothing is $5. The substitution effect of an increase of the price of food to $10 is

Question 7 options:

	-2.07
	-5.00
	-2.53
	-7.07
	-2.93

Answer 1

U(F,C) = F^0.5C^0.5  

U/F = MU_F = 0.5F^{0.5 - 1} C^0.5    

MU_F = 0.5F ^{- 0.5} C^0.5  

U/C = MU_C = 0.5F^0.5 C^{0.5 - 1}  

MU_C = 0.5F^0.5 C^-0.5  

MRS_F,C = ( 0.5F ^{- 0.5} C^0.5  )/)0.5F^0.5 C^-0.5 )  

= C/F  

at optimal choice MRS_F,C = P_F/P_C

C/F =   P_F/P_C

C = F( P_F/P_C )  

Budget constraint

P_FF + P_CC = I  

Put C = F( P_F/P_C ) in Budget constraint

P_FF + P_CC = I  

P_FF + P_C F( P_F/P_C )   = I  

P_FF +  P_FF = I  

2P_FF = I  

F = I/2P_F  

I = 100  

P_F = 5  

P_C = 5  

F = I/2P_F  

F = 100/2(5)  

= 10  

now price of increases to 10

I' = I +  I  

= 10 + (P'_F - P_F)F  

= 100 + (10 - 5)(10)

= 100 + 50  

= 150   

F' = I'/2P'_F  

= 150/2(10)

= 7.5

SE = F'(P'_F , P_C , I ) - F(P_{F ,} P_C , I)

= 7.5 - 10  

= - 2.5