Suppose that Bridget and Erin spend their incomes on two...

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 $U(F, C)=10 F C,$ while Erin's preferences are represented by the utility function $U(F, C)=.20 F^{2} C^{2}$ 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.

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 $U(F, C)=10 F C,$ while Erin's preferences are represented by the utility function $U(F, C)=.20 F^{2} C^{2}$
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.

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Key Concepts

Utility Function

A utility function is a mathematical representation of a consumer's preference ordering over different bundles of goods. It assigns a real number to each bundle such that higher numbers correspond to more preferred combinations, allowing the analysis of consumer choices and satisfaction levels.

Indifference Curve

An indifference curve represents all combinations of goods that yield the same level of utility for a consumer. By plotting these curves, one can visually see how consumers substitute between goods while maintaining constant levels of satisfaction, which is crucial for understanding consumer behavior.

Graphical Analysis of Preferences

Graphical analysis involves plotting indifference curves and other constraints, such as budget lines, on a graph with goods on the axes. This visual tool helps illustrate how different bundles of goods equate in terms of utility and how changes in economic parameters affect consumer choices.

Comparing Preferences

Comparing preferences entails analyzing whether different utility functions reflect similar or dissimilar consumer tastes and substitution patterns. This concept is essential when assessing if distinct utility representations lead to equivalent decision-making behavior or reveal underlying differences in how consumers value goods.

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