Question

A consumer has an income of $90 and they face the following prices: Px =$5 and Py =$3. The consumer prefers good X three as much as good Y and is willing to trade good X and good Y at a constant rate. 1. Write the consumer's utility function that represents their preferences: U(X,Y)=?

Answer 1

The utility function for a consumer who prefers good X three times as much as good Y is U(X,Y) = 3X + Y. With an increase in income, consumers typically purchase more of each good if they are normal goods. Preferences for each good and whether they are normal or inferior dictate individual purchasing decisions.

Step-by-step explanation:

The consumer's utility function that represents their preferences, where the consumer prefers good X three times as much as good Y and is willing to trade them at a constant rate, could be represented as U(X,Y) = 3X + Y. Here, the utility function reflects the greater preference for good X by assigning it a higher weight in utility calculation.

When income increases, and both goods are normal goods, consumers typically purchase more of each. However, if one of the goods is an inferior good, the consumer may purchase less of it with a higher income. The specific choices made along the new budget constraint will depend on each consumer's preferences and the marginal utility of each good. For instance, Manuel might spend more on movies while Natasha might spend more on yogurt as their incomes rise, reflecting their individual preferences.