Question

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) = 10F C, while Erin’s preferences are represented by the utility function U(F, C) = 0.20F 2C 2 .

1. 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).

2. Do you think Bridget and Erin have the same preferences or different preferences? Explain.

Answer 1

Bridget has a utility function U = 10FC, while Erin has a utility function U(F, C) = 0.20F^2C^2 .

1. Below is the graph showing ICB which is the indifference curve for Bridget. This shows the set of points that give Bridget the same level of utility as the bundle (10,5). The utility level along this IC is fixed at U = 10*10*5 = 500. To construct, use the fact that all bundles have U = 500 and this implies the equation of the curve is 500 = 10FC or FC = 50.

The same for Erin is shown on a separate graph. The utility is U(F, C) = 0.20*(10^2)*(5^2) = 500. Hence the curve ICE (E for Erin) has an equation 500 = 0.20*(10^2)*(5^2) or F^2C^2 = 2500.

ICB2 and ICE2 are two other ICs that give both Bridget and Erin the same utility for (15, 8) which is

UB = 10*15*8 = 1200 UE = 0.20*(15^2)*(8^2) = 2880.

The two equations are FC = 120 and F^2C^2 = 14400

2 Bridget and Erin have the same preferences for bundle (10, 5) which is seen from the two indifference curves that entail the same utility of 500. But when the utility bundle (15, 8) is considered, both face a different utility (Bridget has 1200 utils while Erin has 2880 utils).