Consumer Choice: Indifference Theory Chapter 5 LIPSEY & CHRYSTAL ECONOMICS 12e

Introduction In this chapter we look more closely at the determinants of consumer demand. In particular, we discuss the concept of utility and use it to gain insights into how consumers allocate their spending. We show how indifference curves can be used to describe consumers’ tastes and then introduce a budget line to describe the consumption possibilities open to a consumer who has a given income.

Learning Outcomes In particular, you will learn that: Consumers will maximize their overall satisfaction when the marginal utility per pound spent is equal for all products purchased. A theory of demand can be built by focusing on bundles of goods between which the consumer is indifferent. Indifference curves show combinations of goods that give the same level of satisfaction. A budget constraint shows what the consumer could buy with a given income. A consumer optimizes by moving to the highest indifference curve that is available with a given budget constraint.

Learning Outcomes In particular, you will learn that (cont’d): The response to a price change can be decomposed into an income and a substitution effect. For a good to have a negatively sloped demand curve it is necessary (but not sufficient) that it be an inferior good.

The basic assumption here is that consumers are motivated to make themselves as well off as they can, or as economists like to put it: to maximize their satisfaction, or utility.

All units of the same product are identical but the satisfaction that a consumer gets from each unit of a product in not the same. This suggests that the satisfaction that people get from consuming a unit of any product varies according to how many of this product they have already.

Economists and philosophers thinking about consumer choice and satisfaction in the nineteenth century developed the concept of utility and were hence sometimes called utilitarians. But the big breakthrough for economics came in the 1870s with what is known as the marginal revolution, which gave birth to neoclassical economics.

Marginal and total utility The satisfaction a consumer receives from consuming that product is called utility. Total utility refers to the total satisfaction derived from all the units of that product consumed. Marginal utility refers to the change in satisfaction resulting from consuming one unit more or one unit less of that product.

Diminishing marginal utility A basic assumption of utility theory, which is sometimes called the law of diminishing marginal utility, is as follows: The marginal utility generated by additional units of any product diminishes as an individual consumes more of it, holding constant the consumption of all other products.

Maximizing utility We can now ask: what does diminishing marginal utility imply for the way a consumer who has a given income will allocate spending in order to maximize total utility? How should a consumer allocate his or her income in order to get the greatest possible satisfaction, or total utility, from that spending?

If all products had the same price, the answer would be easy. A consumer should simply allocate spending so that the marginal utility of all products was the same. If the marginal utility of all products were not equal then total utility could be increased by a different spending pattern.

For example! If one product had a higher marginal utility than the others, then expenditure should be reallocated so as to buy more of this product, and less of all others that have lower marginal utilities. By buying more, its marginal utility would fall. This continues until the consumer's utility equates to his/her expenditure and utility is maximized.

How does this work if products have different prices? Again, the same principles apply but now the best a consumer can do is to rearrange spending until the last unit of satisfaction per pound spent on each product is the same.

Note! To maximize utility consumers allocate spending between products so that equal utility is derived from the last unit of money spent on each.

Conditions for maximising utility The conditions for maximizing utility can be stated more generally. Denote the marginal utility of the last unit of product X by MUX and its price by pX. Let MUY and pY refer, respectively, to the marginal utility of a second product, Y, and its price. The marginal utility per pound spent on X will be MUX/pX.

The condition required for any consumer to maximize utility is that the following relationship should hold, for all pairs of products:

Note! This is the fundamental equation of utility theory. Each consumer demands each good up to the point at which the marginal utility per pound spent on it is the same as the marginal utility of a pound spent on each other good. When this condition is met, the consumer cannot shift a pound of spending from one product to another and increase total utility.

Consumers choose quantities not prices If we rearrange the terms in previous equation we can gain additional insight into consumer behaviour:

The right-hand side of this equation states the relative price of the two goods. It is determined by the market and is beyond the control of individual consumers, who react to these market prices but are powerless to change them.

The left-hand side of the equation states the relative contribution of the two goods to add to satisfaction if a little more or a little less of either of them were consumed, a choice that is available.

Note! If the two sides of eqn (5.2) are not equal, the consumer can increase total satisfaction by changing the spending pattern. Assume, for example, that the price of a unit of X is twice the price of a unit of Y (pX/pY = 2), while the marginal utility of a unit of X is three times that of a unit of Y (MUX/MUY = 3).

Reducing purchases of Y by two units frees enough purchasing power to buy a unit of X. Since one extra unit of X bought yields 1.5 times the satisfaction of two units of Y forgone, the switch is worth making.

What about a further switch of X for Y? As the consumer buys more X and less Y, the marginal utility of X falls and the marginal utility of Y rises.

In this example the consumer will go on rearranging purchases—reducing Y consumption and increasing X consumption—until the marginal utility of X is only twice that of Y. At this point, total satisfaction cannot be further increased by rearranging purchases between the two products.

Note! It shows that an equilibrium position reached when decision-takers have made the best adjustment they can to the external forces that constrain their choices.

When they enter the market, all consumers face the same set of market prices. When they are fully adjusted to these prices, each one of them will have identical ratios of their marginal utilities for each pair of goods.

A rich consumer may consume more of each product than a poor consumer and get more total utility from them. However, the rich and the poor consumer (and every other consumer who is maximizing utility) will adjust their relative purchases of each product so that the relative marginal utilities are the same for all.

Thus, if the price of X is twice the price of Y, each consumer will purchase X and Y to the point at which his or her marginal utility of X is twice the marginal utility of Y.

Consumers with different tastes will, however, derive different marginal utilities from their consumption of the various commodities. So they will consume differing relative quantities of products

Note! But all will have declining marginal utilities for each commodity and hence, when they have maximized their utility, the ratios of their marginal utilities will be the same for all of them.

Total and Marginal Utility Schedules Number of films attended per month Total utility Marginal utility 0.00 1 15.00 15.00 2 25.00 10.00 3 31.00 6.00 4 35.00 4.00 5 37.50 2.50 6 39.00 1.5 7 40.25 1.25 8 41.30 1.05 9 42.20 0.90 10 43.00 0.80

Total and Marginal Utility Schedules As consumption increases, total utility rises but marginal utility falls. The marginal utilities are the changes in utility when consumption is altered by one unit. For example, the marginal utility of 10m, shown in the entry in the last column, arises because with attendances at the second film total utility increase from 15 to 25 a difference of 10. The data in this table are plotted in the following figure.

Total and Marginal Utility Curves 50 20 40 Utility [£] Utility [£] 15 30 20 10 10 5 2 4 6 8 10 2 4 6 8 10 Quantity of films [attendance per month] [i]. Increasing total utility [ii]. Diminishing marginal utility

Consumer’s Surplus for an Individual 3.00 2.00 Price of milk [£ per glass] 1.00 Market price 0.30 1 2 3 4 5 6 7 8 9 10 Glasses of milk consumed per week

Consumer’s Surplus for an Individual Consumer’s surplus is the sum of the extra valuations placed on each unit above the market price paid for each. This figure is based on the data in the table.Ms. Green pays the red area for the 8 glasses of milk she consumes per week when the market price is £0.30 a glass. The total value she places on these 8 glasses of milk is the entire shaded area (red and green). Hence her consumer’s surplus is the green area.

Consumers’ Surplus for the Market Price D Quantity

Consumers’ Surplus for the Market Price Market price p0 D Quantity q0

Consumers’ Surplus for the Market The area under the demand curve shows the total valuation that consumers place on all units consumed. For example, the total value that consumers place on q0 units is the entire area shaded red and green under the demand curve up to q0. At a market price of p0 the amount paid for q0 units is the red area. Hence consumers surplus is the green area under the demand curve and above p0.

The Utility Theory of Demand MARGINAL UTILITY The Utility Theory of Demand Marginal utility theory distinguishes between the total utility that each consumer gets from the consumption of all units of some product and the marginal utility each consumer obtains from the consumption of one more unit of the product. The basic assumption in utility theory is that the utility the consumer derives from the consumption of successive units of a product diminishes as the consumption of that product increases. Each consumer reaches a utility-maximizing equilibrium when the utility he or she derives from the last £1 spent on each product is equal.

MARGINAL UTILITY Another way of putting this is that the marginal utilities derived from the last unit of each product consumed will be proportional to their prices. Demand curves have negative slopes because when the price of product X falls, each consumer restores equilibrium by increasing his or her purchases of X. The increase must be enough to lower the marginal utility of X until its ratio to the new lower price of X is the same as it was before the price fell. This restores the equality of the ratio to what it is for all other products.

MARGINAL UTILITY Consumers’ Surplus Consumers’ surplus is the difference between [1] the value consumers place on their total consumption of some product and [2] the actual amount paid for it. The first value is measured by the maximum they would pay for the amount consumed rather than go without it completely. The second is measured by market price times quantity.

MARGINAL UTILITY It is important to distinguish between total and marginal values because choices concerning a bit more and a bit less can not be predicted from knowledge of total values. The paradox of value involves confusion between total and marginal values. Elasticity of demand is related to the marginal value that consumers place on having a bit more or a bit less of some product; it bears no necessary relationship to the total value that consumers place on all of the units consumed of that product.

Bundles Conferring Equal Satisfaction Clothing Food A B C D E F 30 18 13 10 8 7 5 10 15 20 25 30

Bundles Conferring Equal Satisfaction 35 a 30 25 g Quantity of clothing per week 20 b 15 c d 10 e f h T 5 5 10 15 20 25 30 35 Quantity of food

Bundles Conferring Equal Satisfaction None of the bundles in the table are obviously superior to any of the others in the sense of having more of both commodities. Since each of the bundles shown in the table give the consumer equal satisfaction, he is indifferent between them. The data in this table are plotted in the corresponding figure.

An Indifference Map Quantity of food per week I5 I4 I3 I2 I1

An Indifference Map A set of indifference curves is called an indifference map. The further the curve from the origin, the higher the level of satisfaction it represents. Moving along the arrow is moving to ever-higher utility levels.

Shapes of Indifference Curves Perfect Substitutes Perfect Complements A good that gives zero utility I2 Left hand gloves Vegetables I2 I1 I2 I1 I1 [i]. Packs of green pins [ii]. Right hand gloves [iii]. Meat

Shapes of Indifference Curves A good that confers a negative utility after some level of consumption A good that is not consumed An absolute necessity I2 I1 a All other goods All other goods All other goods I2 I2 I1 w b I1 f0 [iv]. Water [v]. Food [vi]. Good X

The Equilibrium of a Consumer 35 30 25 Quantity of clothing per week 20 15 10 5 5 10 15 20 25 30 35 Quantity of food per week

The Equilibrium of a Consumer 30 a b 25 c Quantity of clothing per week 20 E 15 10 I5 d I4 5 e I3 I2 f I1 5 10 15 20 25 30 35 Quantity of food per week

The Equilibrium of a Consumer Paul has an income of £150 a week and faces prices of £5 a unit for clothing and £6 a unit for food. A bundle of clothing and food indicated by point a is attainable. But by moving along the budget line to points such as b and c, higher indifference curves can be reached. At E, where the indifference curve I4 is tangent to the budget line, Paul cannot reach a higher curve by moving along the budget line. If he did alter his consumption bundle by moving, for example, from E to d, he would move to the lower indifference curve I3 and thus to a lower level of satisfaction.

An Income-consumption Line Quantity of clothing per week E2 E1 I3 I2 I1 Quantity of food per week

An Income-consumption Line This line shows how a consumer’s purchases react to changes in income with relative prices held constant. Increases in income shift the budget line out parallel to itself, moving the equilibrium from E1 to E2 to E3. The blue income-consumption line joins all these points of equilibrium.

The Price-consumption Line a Price-consumption line E1 Quantity of clothing per week E2 E3 I3 I2 I1 b c d Quantity of food per week

The Price-consumption Line This line shows how a consumer’s purchases react to a change in one price, with money income and other prices held constant. Decreases in the price of food (with money income and the price of clothing constant) pivot the budget line from ab to ac to ad. The equilibrium position moves from E1, to E2 to E3. The blue price-consumption line joins all such equilibrium points.

Value of all other goods Derivation of an Individual’s Demand Curve Price-consumption line E2 Value of all other goods [£ per month] E1 E0 I2 I1 I0 60 120 220 267 400 800 [i] Petrol [litres per month] x 0.75 Price of petrol [£ per month] y 0.50 Demand curve z 0.25 60 120 220

Derivation of an Individual’s Demand Curve The points on a price-consumption line provide the information needed to draw a demand curve. In part (i) Phillip has an income of £200 per month and alternatively faces prices of £0.75, £0.50, and, £0.25 per litre of petrol, choosing positions E0, E1, and E2. The information for the number of litres he demands at each price is then plotted in part (ii) to yield his demand curve. The three points x, y, and z in (ii) correspond to the three equilibrium positions E0, E1 and E2 in part (i).

The Income and Substitution Effects Value of all other goods [£ per week] E1 Substi tution effect I1 b j1 q0 q1 q2 Quantity of petrol [litres per week]