An individual's satisfaction from consuming two goods, Good X and Good Y, is represented by the function U(X, Y) = X * Y. Based on this function, which statement accurately describes the individual's preferences between the following consumption bundles: Bundle A (4 units of X, 9 units of Y) and Bundle B (6 units of X, 6 units of Y)?

Calculating and Interpreting the Marginal Rate of Substitution

An individual consumes two goods, food and clothing. Their preferences are represented by indifference curves that are bowed inward towards the origin. As this individual consumes more food and less clothing while remaining equally satisfied (i.e., on the same indifference curve), what is true about the amount of clothing they are willing to give up to obtain one more unit of food?

Analyzing Consumer Choice Consistency

A consumer is presented with three bundles of goods: Bundle A, Bundle B, and Bundle C. When asked to compare them, the consumer states that they prefer Bundle A over Bundle B, and they prefer Bundle B over Bundle C. However, when asked to compare Bundle A and Bundle C directly, they state a preference for Bundle C over Bundle A. Which of the following statements best analyzes this consumer's expressed preferences?

Calculating the Marginal Rate of Substitution

An individual's preferences for two goods, Good X and Good Y, can be represented by different mathematical functions. Each function results in a unique shape for the set of consumption bundles that provide the same level of satisfaction (indifference curves). Analyze each of the following utility functions and match it to the correct description of the indifference curves it generates.

Evaluating a Trade Offer

The marginal rate of substitution (MRS) at any point on an indifference curve is equal to the slope of the tangent line at that same point.

Consider two utility functions: U1(X, Y) = XY and U2(X, Y) = (XY)², where X and Y are quantities of two different goods, and X > 0, Y > 0. Which of the following statements provides the most accurate analysis of the preferences represented by these two functions?