Suppose that Bridget and Erin spend their incomes on two goo

Suppose that Bridget and Erin spend their incomes on 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 U(F,C) 0.20F C 5. With food on the horizontal axis and clothing on the vertical axis, identify on a graph the set of points that give Bridget the same level of utility as the bundle (10,5). Do the same for Erin on a separate graph. On the same two graphs, identify the set of bundles that give Bridget and Erin the same level of utility as the bundle (15,8). Suppose each individual has an income of $100 and that the price of food is $5 and the price of clothing is $10. Determine the optimal combination of food and clothing consumed by each individual. a. b. c.

Solution

C)

First we find the optimal conbination of food and clothing consumed by Bridget

Bridget utility function;

U(F,C) = 10FC

the consumer equlibrium condition is MUx/ Px = MUy / Py

here the condition is MUf / Pf = MUc / Pc ( as here good X = f (food) and good Y = c (clothing))

where MUf = d(U(F,C))/ df

and MUc = d(U(F,C))/ dc

so MUf = 10C

MUc = 10 F

also Pf = $5 and Pc = $10

put values we get

10C / 5 = 10F / 10

2C = F

put the value of F in the budget constraint of Bridget

Budget Constraint equaltion : Income (M) = Pf * F + Pc * C

put value of Pf, Pc , M and F

100 = 5 * 2C + 10*C

100 = 20C

C* = 5 so the optimal quantity of clothing Bridget consume is 5 units.

similarly we will find the optimal quantity of food consumed by Bridget and then get the optimal combination.

We have equation from consumer equlibrium condition is F = 2C not find the value of C to get the optimal quantity of F.

C = F/2

put this in the budget constraint;

100 = 5 * F + 10 * F / 2

100 = 10F

F* = 10

So the optimal combination of food and clothing Bridget consume is (10, 5).

- This way we will find the optimal combination of food and clothing consumed by Erin.

U(F,C) = 0.20F²C²

MUf = 0.04FC²

MUc = 0.04F²C

put this value in the consumer equilibrium condition, we get,

0.04FC² / 5 = 0.04F² C / 10

solving this, we get

2C = F

so Erin\'s condition is same as Bridget from equilibrium.

his income is also same as Bridget and prices of both goods are same for both it means they have same optimal combination of food and clothing.

2C = F

put the value of F in the budget constraint of Erin

Budget Constraint equaltion : Income (M) = Pf * F + Pc * C

put value of Pf, Pc , M and F

100 = 5 * 2C + 10*C

100 = 20C

C* = 5 so the optimal quantity of clothing Erin consume is 5 units.

similarly we will find the optimal quantity of food consumed by Erin and then get the optimal combination.

We have equation from consumer equlibrium condition is F = 2C not find the value of C to get the optimal quantity of F.

C = F/2

put this in the budget constraint;

100 = 5 * F + 10 * F / 2

100 = 10F

F* = 10

So the optimal combination of food and clothing Erin consume is (10, 5).