Overview
This lecture covers the process of maximizing consumer utility under a budget constraint using marginal utility per dollar, with a worked example involving tacos and meatball subs.
Maximizing Utility: Unlimited Budget
- Samantha chooses between tacos ($2 each) and meatball subs ($4 each) with a utility table provided.
- Without a budget constraint, she maximizes total utility by choosing 6 tacos and 5 subs, where her utility for each good peaks.
Calculating Marginal Utility and Marginal Utility per Dollar
- Marginal utility (MU) = change in total utility for each additional unit.
- For tacos: MU decreases as more tacos are consumed; can eventually become negative (disutility).
- Marginal utility per dollar for tacos = MU divided by $2.
- Marginal utility per dollar for subs = MU divided by $4.
Optimal Bundle with $22 Budget
- Start with $22 and purchase the item with the highest marginal utility per dollar.
- Continue purchasing next highest MU per dollar item, updating the budget until the money runs out.
- Samantha’s optimal bundle: 3 tacos and 4 subs.
Price Change and Law of Demand
- If taco price increases to $3, recalculate MU per dollar for tacos.
- With the new price and same $22 budget, optimal bundle becomes 2 tacos and 4 subs.
- This demonstrates the law of demand: as taco price increases, quantity demanded decreases.
Key Terms & Definitions
- Utility — a measure of satisfaction or happiness from consuming goods.
- Total Utility — total satisfaction from consuming a certain quantity of a good.
- Marginal Utility (MU) — the additional satisfaction from consuming one more unit.
- Marginal Utility per Dollar — marginal utility divided by the good’s price; used to compare across goods.
- Law of Demand — as the price of a good increases, the quantity demanded decreases, all else equal.
Action Items / Next Steps
- Complete the practice assignment on utility maximization before checking the answers.
- Review additional practice problems in the textbook, especially examples at the end of the chapter.