UTILITY ANALYSIS

In this chapter we will discuss: Choice and Utility Theory Law of Diminishing Marginal Utility Equi-Marginal Utility Substitution and Income Effect Indifference Curve Analysis Consumer Surplus

CHOICE AND UTILITY THEORY

It is important to understand the difference between preference and choice. The consumers may have preference when they have a range of products to choose from. Preferences depend upon the consumers likes and dislikes but the final decision is dependent on budget constraints.

UtilityUtility means the satisfaction obtained from the consumption of products and services by consumers. Utility is the satisfaction obtained from good or service. Utility is the benefit or satisfaction that a person gets from the consumption of a good or service The concept of utility is purely subjective (psychological satisfaction)

Measurement of Utility

There are two approaches by which utility can be measured:Cardinal utility approach: Cardinal approach is based on Marshallian school of thought. It has come out with a unit called util to measure the utility. Util reveals how much of money a consumer is willing to pay for a given unit of product.

Measurement of UtilityOrdinal utility approach: This approach is based on the view that utility cannot be measured at all; it can just be ranked in order of preferences. The preference of the customer is based on the choice of products available.Customer is consistent in ranking

Assumptions of Utility Theory

The utility theory is based on some assumptions. Consumers are rational Consumers always prefer more quantity Consumers are ready to make tradeoffs Diminishing marginal rate of substitution

Marginal Utility Analysis .. (Cardinal)Assumptions of Marginal utility AnalysisCardinal measurement of utilityUtilities are independentConstant marginal utility of money.

Total Utility and Marginal UtilityTotal utility can be defined as the amount of utility a person derives from the consumption of a particular product in a given period. Total utility is the amount of satisfaction obtained from entire consumption of a product Total utility is the total benefit that a person gets from the consumption of a good or service. Total utility generally increases as the quantity consumed of a good increases. Total utility = Sum of marginal utilities

Total Utility and Marginal Utility Marginal utility can be defined as the increase in total utility that results from a unit increase in consumption. Marginal Utility: The additional utility a person receives from consuming an additional unit of a good.Marginal utility is the change in total utility obtained by consuming one additional (marginal) unit of a good or service.

Relationship between Marginal . Utility and Total Utility

Quantity of a Product Consumed Total Utility Marginal Utility 0 0 0 1 5 5 2 8 3 3 10 2 4 10 0 5 9 -1 6 7 -2

Relationship between Marginal . Utility and Total UtilityDerivation of Total Utility and Marginal Utility

Chart1

0

40

85

120

140

150

157

160

160

155

145

Total Utility

Sheet1

Q($) TU($) MU

00

14040

28545

312035

414020

515010

61577

71603

81600

9155-5

10145-10

145

Sheet1

Total Utility

Sheet2

($) MU

Sheet3

Chart2

40

45

35

20

10

7

3

0

-5

-10

($) MU

Sheet1

Q($) TU($) MU

00

14040

28545

312035

414020

515010

61577

71603

81600

9155-5

10145-10

145

Sheet1

Total Utility

Sheet2

($) MU

Sheet3

Sheet1

Q($) TU($) MU

00

14040

28545

312035

414020

515010

61577

71603

81600

9155-5

10145-10

145

Sheet1

Total Utility

Sheet2

($) MU

Sheet3

Law of Diminishing Marginal . . UtilityDiminishing marginal utility: As more and more of good is consumed by a consumer, ceteris paribus, beyond a certain point the utility of each additional unit starts to fall. The amount of marginal utility decline as a person consumes more and more of a good.The additional benefit which a person derives from a given increase of his stock diminishes with every increase in the stock that he already has.

Relationship between Marginal . Utility and Total UtilityDerivation of Total Utility and Marginal Utility

Applications of diminishing . marginal utility Explains value paradox: (The Wealth of Nations Adam Smith introduced the diamond-water paradox.) Explains the derivation of Law of demand:Explains the redistribution of income:

Equimarginal Utility

We assume that each consumer maximizes his utility, which means that consumer chooses the most preferred bundle of goods from what is available

Equimarginal PrincipleEquimarginal Principle: The fundamental condition of maximum satisfaction / utility is the equimarginal principle. It states that the consumer having a fixed income and facing given market prices of goods will achieve maximum satisfaction when the marginal utility of the last rupee spent on each good is exactly the same as the marginal utility of the last rupee spent on any other good.

Equimarginal UtilityLaw of equimarginal utility states that the consumer will spend his money on different products in such a way that the marginal utility of each product is proportional to its price. A consumer continues buying a product till its marginal utility is equal to its price. MUx MUy MUE = = Px Py

Equimarginal UtilityA consumer continues buying a product till its marginal utility is equal to its price. Hence the demand curve for a single product is MUx = Px, if it is assumed that the price of the product is fixed.If there is any change in the income level, there is going to be a change in the marginal utility. The consumer goes on consuming or purchasing till the marginal utility of his income or money is equal to both the products. Thus, equilibrium can be achieved at MUx / Px = MUy / Py = MUm

Optimal Purchase Mix: Ice Cream and Hamburger

Sheet1

Q($) TU($) MU

00

14040

28545

312035

414020

515010

61577

71603

81600

9155-5

10145-10

145

QMUIPIMUI/PIMUHPHMUH/PH

1401044567.5

245104.53065

335103.52063.3

4201021562.5

5101011061.7

67100.7661

73100.3360.5

80100060

Sheet1

Total Utility

Sheet2

($) MU

Sheet3

Indifference Curve Analysis An indifference curve is a curve that measures the amount of different goods consumed. Each point on one curve gives exactly the same level of satisfaction for a given consumer. An indifference curve can be said that indifference curve shows the combinations of two products or services to which the customer is indifferent at a particular level of income.

Indifference Curve AnalysisIndifference curves: An indifference curve is a line drawn in a two-dimensional space showing different combinations of two goods from which the consumer draws the same amount of utility and therefore he/she is indifferent about.

Indifference Curve

Indifference CurvesXYU1U2U3U4OSlope = Change in Y/Change in X= MUx/MUy

Assumption of Indifference Curve Analysis RationalityUtility is ordinalConsistency &TransitivityConvexity (Diminishing MRS)

Properties of Indifference curves Indifference curves for two goods are generally negatively slopedIndifference curves are generally convex, reflecting the principle of diminishing returnsIndifference curves never crossIndifference curves that are farther from the origin represent higher levels of utility The slope of an indifference curve reflects the degree of substitutability of two goods for one another

Budget LineA budget line is a line drawn in a two-dimensional space representing a certain level of income with which the consumer can purchase various combinations of two goods at given prices.

Budget LineXYOIncome = Px .Qx + Py. QyI/PyI/PxSlope = Px/Py

Marginal Rate of Substitution Marginal rate of substitution can be defined as the rate at which a customer is willing to substitute one product for the other, maintaining the same level of utility.

Marginal Rate of Substitution

UtilityQuantity of goods X ConsumedQuantity of goods Y ConsumedMRS of X to Y20151----201124:120833:120642:120551:1

Marginal Rate of Substitution

Marginal Rate of Substitution . (Perfect Substitutes) Slope of U curve (MRS)Constant & downward sloping

Marginal Rate of Substitution . . (Perfect Complements) U curves kinked at point representing the "right" mix of consumption

Substitutes & Complements Perfect SubstitutesPerfect ComplementsExample: Mirinda & PepsiExample: Sugar & milk

Consumer Equilibrium

Consumer Equilibrium Can reach point D, but prefer A to DWhy?

Consumer Equilibrium So, point A is clearly is optimal, given budget, prices, tastes & preferences.

Income-Consumption CurveOptimal consumption of X1, X2 as I changesPs, tastes & preferences held constantIf normal goods, then as I increases, outlays on X1, X2 increase as well

X10X2

Income-Consumption CurveAnd, increase income from I2 to I3 and get X1U2U1U3AAAIncome Consumption Curve

Income-Consumption Curve=> As income increases, we can see Demand for inferior good decreasing, given PsIncome Consumption Curve

Consumer Surplus The difference between what a consumer is willing to pay for an addition unit of a good and the market price that he actually pays is referred to as consumer surplus. Consumer surplus can be defined as the difference between what they would like to pay for a product and what they actually pay. The area between the demand curve and the price line is the total consumer surplus.

Why Consumer Surplus We pay same price for each good. Law of Diminishing Marginal Utility

Consumer Surplus Consumer Surplus = Total willing to pay - Actual pay 27 12 = 15

Qty.Willing to payActual pay172262352442532622

Consumer Surplus PriceDQx0P

Applications of Consumer Surplus

Consumer surplus is useful for designing government policies and implementing welfare programs. Consumer surplus helps the monopolist in fixing the price of a commodityConsumer surplus also advocates for international trade. Consumer surplus can also be used to measure the health of an economy.

any ?

Consumer SurplusConsumer Surplus = Prepared to pay actual payConsumer Surplus = Total Utility amount spentConsumer Surplus = Total utility P* Qd

Consumer Surplus Total willing to pay - Actual pay = Consumer Surplus 28 12 = 16

QtyWilling to payActual pay172262352442532622

Applications of Consumer Surplus

Consumer surplus is useful for designing government policies and implementing welfare programs. Consumer surplus helps the monopolist in fixing the price of a commodityConsumer surplus also advocates for international trade. Consumer surplus can also be used to measure the health of an economy.

any ?

Income-Consumption CurveCan show typical Demand curve shiftsNote that P2 held constantJust changing income, I

Income-Consumption CurveCan show typical Demand curve shifts with normal good

Income-Consumption CurveSo, increase I from I1 to I2 and get

Income-Consumption CurveAnd, increase income from I2 to I3 and get X1U2U1U3AAAIncome Consumption Curve

Income-Consumption CurveIf inferior goods, thenAs income increases, outlays on goods, say X2 here, actually decrease Occurs typically over some, not the entire, range of consumptionNote shapes of indifference curves

Income-Consumption CurveE.g. : SPAM, Texas wines, as before...

Income-Consumption CurveAgain, can show typical Demand curve shifts with Income-Consumption curve

Income-Consumption Curve=> As income increases, we can see Demand for inferior good decreasing, given PsIncome Consumption Curve

***************E.g. SPAM, Texas wines, as before

**