Chapter 7 Utility Maximization PDF

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Chapter 7: Utility Maximization Sunday, August 9, 2020

3:08 AM

CHAPTER 7 (Overview)

7.1 Law of Diminishing Marginal Utility • Law of diminishing marginal utility - added satisfaction declines as a consumer acquires additional units of a given product. ○ The more of that product they obtain, the less they want still more of it. ○ i.e. a consumer's desire for an automobile, when they have non, is very strong. But desire for a second car is less intense.

Chapter 7 Sections ✓ Section 7.1 ✓ Section 7.2 ✓ Section 7.3 ✓ APPENDIX

• Terminology ○ Utility - satisfaction or pleasure one gets from consuming a good or service. ○ "Utility" and "usefulness" are not synonymous ○ Utility is subjective, varies from person to person ○ Utility is difficult to quantify ▪ But for the purpose of illustration we assume that people can measure satisfaction with units called utils. ▪ i.e. a consumer may get 100utils of satisfaction from a smoothie, 10 utils satisfaction from a candy bar ▪ These imaginary units of satisfaction are convenient for quantifying consumer behaviour for explanatory purposes.

Quick Review 7.1

• Total Utility and Marginal Utility ○ Total utility and marginal utility are related, but different ideas. ○ Total utility - total amount of satisfaction or pleasure a person derives from some specific quantity. (i.e. 10 units) ○ Marginal utility - extra satisfaction a consumer realizes from an additiona product (from an extra 11th unit) ▪ Change in total utility that results from the consumption of 1 more un ○ Figure 7.1 demonstrate the relation between total utility and marginal utility ▪ Column 2 shows the total utility associated wit ▪ Column 3 shows marginal utility, the total chan

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▪ TU increases by a diminishing amount in the fir reaches a maximum (additional 6th unit), then starts declining. ○ In Figure 7.1b, ▪ MU is positive but diminishes through the first five □ because TU increases at a declining rate ▪ MU is zero for the 6th unit □ because it doesn’t change TU ▪ MU becomes negative with 7th unit and beyond □ Because TU is falling

✓ Utility is the benefit or satisfaction a person receives from consuming a good or a service ✓ The law of diminishing marginal utility indicates that gains in satisfaction become smaller as successive units of a specific product are consumed. ✓ Diminishing marginal utility provides a simple rationale for the law of demand. KEY CONCEPTS - Total Utility and Marginal Utility DEFINITIONS ✓ Law of Diminishing Marginal Utility - Marginal Utility and Demand ✓ Utility ✓ Total Utility ✓ Marginal Utility Quick Review 7.2 ✓ The theory of consumer behaviour assumes that, with limited income and a set of product prices, consumers make rational choices on the basis of well-defined preferences ✓ A consumer maximizes utility by allocating income so that the marginal utility by allocating income so that the marginal utility per dollar spent is the same for every good purchased. ✓ A downsloping demand curve can be derived by changing the price of one product in the consumer-behaviour model and noting the change in the utility-maximizing quantity of that product demanded. KEY CONCEPTS ✓ By providing insights on the income effect and substitution a price decline, - Consumer Choice and the effect BudgetofConstraint the utility-maximization model-helps explain whyper demand Marginal Utility Dollarcurves are downsloping. - Decision-Making Process - Deriving the Demand Schedule and Curve DEFINITIONS ✓ Utility-Maximizing Rule - Income and Substitution Effects ✓ Consumer Equilibrium

• Marginal Utility and Demand ○ The law of diminishing marginal utility explains why demand curves have downward slopes. ▪ Consumer will buy additional units only if its price falls ○ Consumer would rather spend additional dollars on products that provide more utility, not less. ▪ i.e. additional tacos with less utility are not worth buying unless price declines ▪ When MU is negative, firms have to pay you to consumer another product!

Learning Objectives 1. Define and explain the relationship between total utility, marginal utility, and law of diminishing marginal utility.

- The law of diminishing marginal utility states that beyond a certain quantity, additional units of a specific good will yield declining amounts of extra satisfaction to a consumer.

○ Thus, diminishing marginal utility supports the idea that price must decrease in order for quantity demand to increase.

7.2 Theory of Consumer Behaviour

2. Describe how rational consumers maximize utility by comparing the marginal utility-to-price ratios of all the products they could possibly purchase

• Diminishing marginal utility also explains how consumers allocate their money incomes among the many G&S available.

- The utility-maximization model assumes that the typical consumer is rational and acts on the basis of well-defined preferences. Because income is limited and goods have prices, the consumer cannot purchase all the goods and services they might want. The consumer therefore selects the attainable combination of goods that maximizes their utility or satisfaction.

Consumer Choice and the Budget Constraint  We will assume that the situation for the typical consumer has the following dimensions. • Rational behaviour ○ Consumer is rational, tries to use their money income to maximize their utility by engaging in rational behaviour.

- A consumer's utility is maximized when income is allocated so that the last dollar spent on each product purchased yields the same amount of extra satisfaction. Algebraically, the utility-maximizing rule is fulfilled when Uo

• Preferences ○ Each consumer had clear-cut preferences for certain of the G&S available in the market ○ Good idea of how much MU they will get from successive units of the various products they might purchase.

• Consumer equilibrium - when consumer had "balance" his margins using the utility-maximizing rule and has no incentive to alter his expenditure pattern. ○ Any person who achieved consumer equilibrium would be worse off, TU would decline, if there were any alteration in the bundle of goods purchased, providing there is no change in taste, income, products, or prices.

Numerical Example

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- The utility-maximizing rule and the demand curve are logically consistent. Because marginal utility declines, a lower price is needed to induce the consumer to buy more of a particular product.

4. Discuss how the utility-maximization model helps highlight the income and substitution effect of a price change. - The utility-maximization model illuminates the income and substitution effects of a price change, The income effect implies that a decline in the price of a product increases the consumer's real income and enables the consumer to buy more of that product with a fixed money income. The substitution effect implies that a lower price makes a product relatively more attractive and therefore increases the consumer's willingness to substitute it for other products.

 Consumer must choose the personally satisfying mix of goods and services. Utility-Maximizing Rule • Utility-maximizing rule - Consumer should allocate their money income so that the last dollar spent on each product yield the same amount of extra (marginal) utility to maximize satisfaction.

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3. Explain how a demand curve can be derived by observing the outcomes of price changes in the utility-maximization model.

• Budget constraint ○ At any point in time the consumer has a fixed, limited amount of money income ○ Every consumer faced a budget constraint • Prices ○ Goods are scare relative to the demand for them, every good carries a price tag ○ We assume price of each good is unaffected by the amount of it bought by any particular person

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Table 7.1

phenomena can be explained by applying

our can explain many real world phenomena, popular consumer goods like the iPad that s, the overconsumption of products like health rices, and people's preference for gifts of cash objects of the same monetary value.

there were any alteration in the bundle of goods purchased, providing there is no change in taste, income, products, or prices.

Numerical Example  Suppose consumer Holly is analyzing which combination of two products she should purchase with her fixed daily income of $10 ○ Table 7.1 column 2a shows MU she will derive from each successive units of A and column 3a shows the same for B Marginal Utility per Dollar ○ To see how utility maximizing rule works, we must put the MU info in columns 2a and 3a on a per-dollar spent basis ▪ A consumer choice are not just influenced by extra utility from A but also by how many dollars (or B) she must give up to obtain additional units of A (opportunity cost) ▪ To make amounts of extra utility derived from differently prices goods comparable, we find MU/Price Decision-Making Process ○ Concentrating on columns 2b and 3b, we find Holly should first spend $2 on the first B because its MU/$ or 12 utils is higher than A's 10 util. But now both 1st A and 2nd B is 10 utils, so Holly buys both of them. ○ Now Holly has $5 remaining, Holly can spend the next $2 on a 3rd B because MU/$ is 9 compare to a 2nd A of 8 utils. ○ Now both 2nd A and 4th B provide 8 utils/$, Holly buys both and $10 is exhausted. ○ The utility-maximizing combination of goods attainable by Holly is 2As 4Bs, and a total of 96 utils of satisfaction is obtained.  Note that saving can be regarded as a "commodity" that yields utility too. Inferior Options ○ Holly can obtain other combinations of A and B but none will yield as much total utility as 2A 4Bs. ○ Other combinations are either unobtainable with limited money income or do not exhaust the money income ▪ And therefore do not yield the maximum utility attainable  Algebraic Generalization ○ Economist generalize utility-maximizing rule by saying a consumer will maximize her satisfaction when she allocates her money income so that last dollar spent on each product yields equal amounts or additional, or marginal, utility. ○ Our utility-maximizing rule merely requires that these ratios be equal for the last dollar spent on A and B U o oduct

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○ Table 7.1 shows us that the combination of 2A and 4B fulfills these conditions in that uti s

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all $10 are spent.

○ If equation is not fulfilled, then some reallocation of the consumer's expenditures between A and B (from low to high MU/$ product) will increase the consumer's total utility ▪ i.e. if consumer spend $10 on 4A 3B,

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▪ Last dollar spend on A provides only 6 utils, while last dollar spend on B provides 9 ▪ So consumer can increase total satisfaction by purchasing more of B and less of A ▪ As $ reallocated from A to B, MU/$ of A will increase and MU/$ B will decrease, consumer equilibrium is achieved.

Utility Maximization and the Demand Curve  Deriving the Demand Schedule and Curve ○ We can derive a consumer's demand schedule for oranges by considering alternative prices at which oranges might be sold and then determining the quantity the consumer will purchase. ○ We already know given tastes, income, and prices of other Holly will purchase 4 oranges at $2. ○ Now let's assume price of oranges falls to $1 ▪ The MU/$ data of column 3b in Table 7.1 will double because price of oranges has been halved. ▪ Holly's new utility-maximizing combination is 4A 6B ▪ We can sketch the downward-sloping demand curve for oranges Do ○ This links the utility-maximizing behaviour of a consumer and the downsloping demand curve for a particular product.  Income and Substitution Effects ○ Income effect - impact that change in the price of a product has on a consumer's real income and consequently Qd of a good. ▪ Decline in price of ranges increases Holly's real income. ▪ Before Holly maximized utility and achieved consumer equilibrium by spending $10. □ Now Holly would have to only spend $6 instead of $10 to buy the same combination □ The lower price of oranges has freed up more income. □ It is quite likely that the increase in real income caused by reduction of price of oranges will cause Holly to buy more oranges than before the price reduction.

▪ When price of oranges falls, income effect causes Holly to buy more oranges. ○ Substitution effect - impact that a change in a product's price had on its relative expensiveness and consequently on Qd.

▪ Before the price drop of orange, Holly was in equilibrium when purchasing 2A 4B U o a es o ices o a es o

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▪ After the price of oranges declines from $2 to $1

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objects of the same monetary value.

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▪ The last dollar spent on oranges now yields a greater utility (16 utils) than does on apples (8 utils) ▪ This will lead Holly to substitute purchases away from apples and toward oranges to restore consumer equilibrium. ▪ When the price of oranges declines, the substitution effect causes Holly to buy more oranges.

7.3 Applications and Extensions  iPad ○ Apple's introduction of the iPad severely disrupted consumer equilibrium ○ Consumers concluded that iPads had a higher marginal-utility-to-price ratio (=MU/P) than for other products ○ Although most people's marginal utility of a 2nd or 3rd iPad relative to price is quite low, but Apple continued to enhance iPads, enticing buyers of older models to buy new models. ○ New products succeed by enhancing consumer's total utility.

 The Diamond-Water Paradox ○ Adam Smith developed this model ○ Why would water, essential to life, be priced below diamonds, which have much less usefulness? ○ The paradox is resolved when we acknowledge that ▪ Water is in great supply relative to demand thus have lower price. ▪ Diamonds are rare, supply is relative small to demand, so they have higher price. ▪ MU of the last unit of water consumed is very low - (generating electricity, irrigating crops, heating buildings, watering lawns, quenching thirst, and so on). Consumption is expanded until MU equals its low price. ▪ Few diamonds are purchased because of their prohibitively high price, MU remains high. U o ate ice o ate

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▪ Although the MU of the last unit of water consumed is low and the MU of the last diamond purchased is high, the TU of water is very high (sum MU of all gallons consumed) and the TU of diamonds are low (few are bought) ▪ Thus, water has much more TU than diamonds even though price of diamonds greatly exceeds the price of water. □ These relative prices relate to MU not TU.  Opportunity Cost and the Value of Time ○ Both consumption and production take time. ○ Time is a valuable commodity ○ By using an hour for leisure or in consumption activities, the individual incurs the opportunity cost of forgone income. ▪ He or she sacrifices the $6, $10, or $50 that could have earned by working ▪ i.e. Linden who consider buying a round of golf $30 and a concert $40. □ The golf game takes more time than the concert 4 hours and 2 hours, respectively. □ If Linden's time is worth $10 per hour, then the "full price" of the golf game is $70 (= $30 + $40) □ We find that "full price" of concert is $60, which is less than the full price of golf game. ▪ i.e. CEO find it cheaper to fly, unskilled worker or retiree whose time has little market value would prefer bus rides.

 Medical Care Purchases ○ When people pay less for healthcare, they tend to purchase it more ○ Similar reasoning applies to buffet meals, you tend to eat more. Its MU is positive and its "price" is zero.  Cash and Noncash Gifts ○ People prefer cash gifts because noncash gifts may not match the recipient's preference. ○ Marginal Utility is lost because with cash gifts the recipient could use it to buy something else. ○ To avoid such utility lost ▪ Some people set up gift registries to help match up their wants to the noncash gifts received. ▪ Obtain cash refunds or exchanges for gifts so they can buy goods that provides more utility. ▪ "Recycle gifts" by giving them to someone else at later time.

Chapter 7 APPENDIX  Cardinal utility is measured in units such as 1, 2, 3, and 4, can be added, subtracted, multiplied, and divided. ○ Allow precise quantification of the marginal utility which utility-maximizing rule depends on. ○ Reality is, measuring cardinal utility is highly difficult.  To avoid measurement problem, economists develop an alternative explanation of consumer behaviour and equilibrium in which cardinal measurement is not required. ○ In this analysis, consumer must simply rank various combinations of goods in terms of preference. ○ i.e. Sally can report she prefers 4 units of A to 6 units of B without putting a number on how much she likes either option.  Indifference curve analysis - the model of consumer behaviour that is based upon ordinal utility rankings. ○ Consist of two main elements: Budget lines and indifference curves. The Budget Line: What is Attainable ○ Budget line - or budget constraint, is a schedule or curve showing various combinations of two products a consumer can purchase with a specific money income. ○ Every point in Figure 1 represents a possible combination of A and B, including fractional b quantities. ○ The slope measures Pb/Pa = 2/3, which means the consumer must forgo 2 units of A to buy a3 units of B

○ The budget line has two other significant characteristics:

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1. Relate how the indifference curve model of consumer behaviour derives demand curves from budget lines, indifference curves, and utility maximization. - The indifference curve approach to consumer behaviour is based on the consumer's budget line and indifference curves. - The budget line shows all combinations of two products that the consumer can purchase, given product prices and his or her money income. A change in either product prices or money income moves the budget line. - An indifference curve shows all combinations of two products that will yield the same total utility to a consumer. Indifference curves are downsloping and convex to the origin. - An indifference map consists of a number of indifference curves; the farther from the origin, the higher the total utility associated with a curve.

- The consumer is in equilibrium (utility is maximized) at the point on the budget line that lies on the highest attainable indifference curve. At that point the budget line and indifference curve are tangent. - Changing the price of one product shifts the budget line and determines a new point. A downsloping demand curve can be determined by plotting the Figureequilibrium 1 points.

rankings. ○ Consist of two main elements: Budget lines and indifference curves. The Budget Line: What is Attainable ○ Budget line - or budget constraint, is a schedule or curve showing various combinations of two products a consumer can purchase with a specific money income. ○ Every point in Figure 1 represents a possible combination of A and B, including fractional b quantities. ○ The slope measures Pb/Pa = 2/3, which means the consumer must forgo 2 units of A to buy a3 units of B ○ The budget line has two other significant characteristics: ▪ Income changes □ ↑ in income, budget line shifts → □ ↓ in income, budget line shifts ← ▪ Price changes □ ↓ price, budget line shifts → □ ↑ price, budget line shifts ← Ub t e ui ib iu ○ If Pb changes while Pa and money income remain constant. Ua ▪ If Pb ↓ lower end of the budget line fans outward. ▪ If Pb ↑ lower end of the budget line fans inward to the left. ▪ The line ...