Cindy's tennis club raises its price of an hour of tennis...

Cindy's tennis club raises its price of an hour of tennis from $\$ 5$ to $\$ 10$, other things remaining the same. a. List the combinations of hours spent playing golf and tennis that Cindy can now afford and her marginal utility per dollar from golf and from tennis. b. How many hours does Cindy now spend playing golf and how many hours does she spend playing tennis?

Cindy's tennis club raises its price of an hour of tennis from $\$ 5$ to $\$ 10$, other things remaining the same. a. List the combinations of hours spent playing golf and tennis that Cindy can now afford and her marginal utility per dollar from golf and from tennis.
b. How many hours does Cindy now spend playing golf and how many hours does she spend playing tennis?

Key Concepts

Budget Constraint

The budget constraint represents the combinations of two goods (or activities) that a consumer can purchase given their income and the prices of the goods. It is depicted as a line or equation showing the trade-off between the goods, where spending more on one good necessitates spending less on the other. In the context of utility theory, shifts in prices will rotate or shift this constraint, altering the set of affordable combinations available to the consumer.

Marginal Utility per Dollar

Marginal utility per dollar is calculated by dividing the marginal utility of a good by its price and measures the additional satisfaction a consumer receives per unit of currency spent on that good. Consumers use this concept to allocate their resources efficiently; when maximizing utility, they equalize the marginal utility per dollar across all goods, ensuring no reallocation of spending could yield higher total utility.

Utility Maximization

Utility maximization is the process by which a consumer chooses the combination of goods that maximizes their overall satisfaction subject to their budget constraint. This involves equating the marginal utility per dollar across all goods, which ensures that resources are allocated in a way that no additional unit of currency spent on one good would produce a greater increase in overall utility than if it were spent on another good.

Adjustment to Price Changes

When the price of one good changes, the budget constraint alters, leading to a new optimal consumption choice. This adjustment can be analyzed by examining how the marginal utility per dollar for the good that experienced the price change compares with that of other goods, and by determining the new point of tangency between the indifference curve and the modified budget constraint. This process helps explain the consumer's substitution of one good for another in response to price changes.

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