# Measuring Utility How much utility do you receive from eating donuts?

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6 Consumers, Producers, and the Efficiency of Markets
What is utility and how is it measured? What is the Law of Diminishing Marginal Utility? How do consumers maximize utility? How is utility related to the demand curve? What is consumer surplus? How is it related to the demand curve?

Measuring Utility How much utility do you receive from eating donuts?

Law of Diminishing Marginal Utility
The more of a good a person consumes, the smaller the increase in total utility from consuming the good, all else equal In other words, marginal utility falls as we consume more and more donuts

Finding the Optimal Bundle: An Example
Assume: Isaac has \$10 per week to spend on donuts and cookies Price of a donut = \$1.00 Price of a cookie = \$2.00 How many of each should Isaac buy? Finding the Optimal Bundle: An Example

Finding the Optimal Bundle: An Example
Donuts Q TU MU MU per \$ ---- 1 10 2 19 3 27 4 34 Cookies Q TU MU MU per \$ ---- 1 25 2 45 3 60 4 70

The Consumer Optimum Occurs where the marginal utility per dollar spent on each good is equal

The Law of Demand What happens if the price of a cookie rises to \$3.00?

Finding the Optimal Bundle: An Example
Donuts Q TU MU MU per \$ ---- 1 10 2 19 9 3 27 8 4 34 7 Cookies Q TU MU MU per \$ ---- 1 25 2 45 20 3 60 15 4 70 10

The Law of Demand What happens if the price of a cookie rises to \$3.00? Quantity of cookies demanded falls

A C T I V E L E A R N I N G 1: Optimal bundle
Find the optimal quantity of both goods if the individual has \$5 per week to spend on apples and oranges and they each are priced at \$1: Apples Q TU 1 20 2 35 3 48 4 58 5 66 Oranges Q TU 1 19 2 32 3 40 4 45 5 49 9

Willingness to Pay (WTP)
A buyer’s willingness to pay for a good is the maximum amount the buyer will pay for that good. WTP measures how much the buyer values the good. Name WTP Anthony \$250 Chad 175 Flea 300 John 125 Example: 4 buyers’ WTP for an iPod

WTP and the Demand Curve
Q: If price of iPod is \$200, who will buy an iPod, and what is quantity demanded? Name WTP Anthony \$250 Chad 175 Flea 300 John 125

WTP and the Demand Curve
Derive the demand schedule: P (price of iPod) Who Buys? Qd \$301 & up Nobody 251 – 300 Flea Name WTP Anthony \$250 Chad 175 Flea 300 John 125 176 – 250 Anthony, Flea 126 – 175 Chad, Anthony, Flea 0 – 125 John, Chad, Anthony, Flea

Consumer Surplus (CS) CS = WTP – P
Consumer surplus is the amount a buyer is willing to pay minus the buyer actually pays: CS = WTP – P Suppose P = \$260. Flea’s CS = \$300 – 260 = \$40. The others get no CS because they do not buy an iPod at this price. Total CS = \$40. Name WTP Anthony \$250 Chad 175 Flea 300 John 125

A C T I V E L E A R N I N G 2: Consumer surplus
demand curve P \$ A. Find marginal buyer’s WTP at Q = 10. B. Find CS for P = \$30. Suppose P falls to \$20. How much will CS increase due to… C. buyers entering the market D. existing buyers paying lower price Q 14

A More Formal Utility Analysis
Economists can be more specific about the ways in which consumers maximize utility This material is from the Appendix to Chapter 6

The Budget Constraint: What the Consumer Can Afford
Two goods: pizza and Pepsi A “consumption bundle” is a particular combination of the goods, e.g., 40 pizzas & 300 pints of Pepsi. Budget constraint: the limit on the consumption bundles that a consumer can afford The two-good assumption greatly simplifies the analysis without altering the basic insights about consumer choice. If your students remember the Production Possibilities Frontier, you might tell them that a budget constraint is, in essence, a “consumption possibilities frontier” for the consumer: it shows all combinations (bundles) of the two goods that the consumer can afford to buy.

A C T I V E L E A R N I N G 3: Budget constraint
The consumer’s income: \$1,000 Prices: \$10 per pizza, \$2 per pint of Pepsi A. If the consumer spends all his income on pizza, how many pizzas does he buy? B. If the consumer spends all his income on Pepsi, how many pints of Pepsi does he buy? C. If the consumer spends \$400 on pizza, how many pizzas and Pepsis does he buy? D. Plot each of the bundles from parts A-C on a diagram that measures the quantity of pizza on the horizontal axis and quantity of Pepsi on the vertical axis, then connect the dots. 17

The Slope of the Budget Constraint
Pepsis From C to D, Y (“rise”) = –100 Pepsis X (“run”) = +20 pizzas Slope = –5 Consumer must give up 5 Pepsis to get another pizza. C D Pizzas

The Slope of the Budget Constraint
The slope of the budget constraint equals the rate at which the consumer can trade Pepsi for pizza the opportunity cost of pizza in terms of Pepsi the relative price of pizza

A C T I V E L E A R N I N G 4: Exercise
Pepsis Show what happens to the budget constraint if: A. Income falls to \$800 B. The price of Pepsi rises to \$4/pint. Pizzas 20

A C T I V E L E A R N I N G 5: Inferior vs. normal goods
An increase in income increases the quantity demanded of normal goods and reduces the quantity demanded of inferior goods. Suppose pizza is a normal good but Pepsi is an inferior good. Use a diagram to show the effects of an increase in income on the consumer’s optimal bundle of pizza and Pepsi. Instead of merely showing students the diagram for the case where one of the goods is inferior, let’s just remind them of the definition and see if they can figure out how to draw the diagram. 21

Income and Substitution Effects
A fall in the price of Pepsi has two effects on the optimal consumption of both goods. Income effect A fall in the price of Pepsi boosts the purchasing power of the consumer’s income, allowing him to reach a higher indifference curve. Substitution effect A fall in the price of Pepsi makes pizza more expensive relative to Pepsi, causes consumer to buy less pizza & more Pepsi.

The Substitution Effect for Substitutes and Complements
The substitution effect is huge when the goods are very close substitutes. If Pepsi goes on sale, people who are nearly indifferent between Coke and Pepsi will buy mostly Pepsi. The substitution effect is tiny when goods are nearly perfect complements. If software becomes more expensive relative to computers, people are not likely to buy less software and use the savings to buy more computers.

A C T I V E L E A R N I N G 6: Income & substitution effects
The two goods are skis and ski bindings. Suppose the price of skis falls. Determine the effects on the consumer’s demand for both goods if income effect > substitution effect income effect < substitution effect Which case do you think is more likely? To answer the last question, students will need to recognize that skis and ski bindings are complements, so the substitution effect is not likely to be very strong. Even if they do not recognize this, they should still be able to answer the rest of the questions on this slide. 24

One Last Issue Since an individual knows his or her own preferences better than anyone else, is cash the best gift for someone?

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