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Magazine Chapter 3: Q5. (page 128)
Suppose that Bridget and Erin spend their incomes on two goods, food (F) and clothing (C). Bridget鈥檚 preferences are represented by the utility function U(F, C) = 10FC, while Erin鈥檚 preferences are represented by the utility function U(F,C) = 0.20F2C2.
a. 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.
b. 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).
c. Do you think Bridget and Erin have the same preferences or different preferences? Explain.
Short Answer
a. Bridget and Erin have the same level of satisfaction for the given utility functions when their consumption bundle is (10,5).
Bridget:
Erin:
b. Bridget and Erin have a different level of satisfaction for the given utility functions when their consumption bundle is (15,8).
Bridget:
Erin:
c. Bridget and Erin will prefer (10,5) since their satisfaction levels are the same.
Erin will prefer (15,8), while Bridget will choose a different combination of food and clothing where her utility will be greater than or equal to Erin.
Step by step solution
Utility of Bridget and Erin when consumption bundle is (10,5)
The numerical score or a cardinal scale representing the satisfaction a consumer gets from a market basket gives the utility for that consumer.
Bridget鈥檚 utility will be:
U(F, C) = 10FC
= 10 x 10 x 5 = 500
The above indifference curve of Bridget represents all bundles of food and clothing that provide the same level of satisfaction. In other words, the IC curve represents all combinations of goods where Bridget鈥檚 utility is 500.
Similarly, Erin鈥檚 utility will be:
U(F,C) = 0.20F2C2
= 0.20 x 102 x 52 = 500
The above indifference curve of Erin represents all bundles of food and clothing that provide the same level of satisfaction. In other words, the IC curve represents all combinations of goods where Erin鈥檚 utility is 500.
Bridget and Erin have the same level of satisfaction for the given utility functions when their consumption bundle is (10,5).
Utility of Bridget and Erin when consumption bundle is (15,8)
Bridget鈥檚 utility will be:
U(F, C) = 10FC
= 10 x 15 x 8 = 1200
The above indifference curve of Bridget represents all bundles of food and clothing that provide the same level of satisfaction. In other words, the IC curve represents all combinations of goods where Bridget鈥檚 utility is 1200.
Similarly, Erin鈥檚 utility will be:
U(F,C) = 0.20F2C2
= 0.20 x 152 x 82 = 2880
The above indifference curve of Erin represents all bundles of food and clothing that provide the same level of satisfaction. In other words, the IC curve represents all combinations of goods where Erin鈥檚 utility is 2880.
Bridget and Erin have a different level of satisfaction for the given utility functions when their consumption bundle is (15,8).
Bridget and Erin’s preferences
When the satisfaction levels are the same, the market basket preferences will be the same for two consumers.
So, for the consumption bundle (10,5), despite different utility functions, Bridget and Erin have equal satisfaction levels or the utility, 500. One can conclude that Bridget and Erin have the same preferences for the bundle.
When the consumption bundle is (15,8), their utilities are different. Bridget鈥檚 utility is less than Erin鈥檚. So, Bridget will prefer a different combination bundle of food and clothing.
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