Question

1. Suppose that Bridget and Erin spend their incomes on only two goods, food (F) and clothing (C). Bridget’s preferences are represented by the utility function U(F,C)=10FC, while Erin’s preferences are represented by the utility function UF,C=5F2C.
   1. With the market basket F=2 and C=5, both Bridget and Erin get 100 unit of utility. Is it correct to say that Bridget and Erin have the same preference (i.e. their indifference curves are the same)? Explain your answer.

2. Would you agree that Erin enjoys clothing more than Bridget does when F<4? Apply the concept and derivation of marginal rate of substitution and provide your support to the conclusion.

Answer 1

(a) Both have different utility functions, and their utility curve for U=100 intersects at where F=2 and C=5. Yet the Bridget and Erin's individual utility curves would not intersect for different utility levels, but comparing both of their Utility functions, they would intersect where
UR=US
or
10 FC = 5
or . We have the required graphs as below.

2 07

We can see that Bridget's IC (B) is different from Erin's IC (E), its just that when both are at utility level U=100, their IC's intersects at point A, where F=2 and C=5. We can even algebraically see that they have different sets of preferences for the same utility, only except at point A.

16-- Ç=5 LC=4 C = 3 B's utility 2 E'S Utility F#2

Here we can see different ICs (U = 100,80,60) of B and E, and they intersect at F=2 (as solved above), and at C = 5,4,3.

[Note that we can compare different MRS also to state that both have different ICs. At F=2 and C=5, Bridget is willing to forgo
MRSE =
units of C for adding a unit F, while Erin is willing to forgo
MRSE =
units of C for adding a unit F. But MRS seems to be required in the next part, so MRS is used in part b.]

(b) Bridget's MRS would be as
dU = d(10FC)
or
0 = 10CdF + 10 FC
or $\frac{\mathrm{d} C}{\mathrm{d} F} = - \frac{C}{F}$ , ie
MRSB =
.

Erin's MRS would be as
dU = d(5F-C)
or
0 = 5C(F) +5F-DC
or
0 = 10FCdF +5FdC
or
1-=
, ie
MRSE =
.

We have
MRSE > MRSE
since $2 \left (\frac{C}{F} \right ) > \left ( \frac{C}{F} \right )$ or $\frac{2C}{F} > \frac{C}{F}$ for any combination of C and F. This means that Erin is willing to forgo more units of Cs for an additional unit F, than Bridget. This would mean that Erin enjoys clothes less than Bridget, since Erin can forgo more clothes than Bridget for the same amount of food, to remain at the same utility level. Moreover, it doesn't depend on whether F<4 or not, but is true for all possible combinations of F and C.