Consumer Choice Indifference Theory The basic assumption here

Consumer Choice: Indifference Theory

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 is not the same. This suggests that the satisfaction that people get from consuming a unit of any product varies according to how many units 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 1870 s with what is known as the marginal revolution, which gave birth to neoclassical economics.

Decision Making Process of the consumer: 1. Preference Set: It is a comprehensive set of all preferences of the consumer. 2. Opportunity set: It consists of combinations of the two goods that the consumer can buy given that there is a limited income that one can spend on these goods.

Preference set under these assumptions: 1. Assumption of completeness: When a consumer is confronted with any of the two goods or two basket of goods, she is able to express that she prefers one or the other or whether she is indifferent. 2. Assumption of Transitivity: If a consumer prefers A to B and prefers B to C, then she will prefer A to C

3. Assumption of Non-Satiation: A rational consumer prefers more of a good to less of the good.

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.

Total and Marginal Utility Schedules Number of films attended per month Total utility Marginal utility 0 0. 00 1 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 10 m, 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 Utility [£] 50 40 20 30 15 20 10 10 5 0 2 4 6 8 10 0 2 4 6 8 Quantity of films [attendance per month] [i]. Increasing total utility [ii]. Diminishing marginal utility 10

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?

Optimization – Cardinal Approach Optimization Rule 1: When unlimited quantity of a good is available for no cost and the individual has to consume successive units of the commodity at the same point in time, a rational consumer willmaximise total utility by consuming till the point where marginal utility is zero. MUx = 0

Total and Marginal Utilities from Ice Cream Consumption for Individual Units Total Utility Marginal Utility 1 10 10 2 18 8 3 23 5 4 25 2 5 25 0 6 23 -2 7 18 -5

Optimization Rule 2: When only one good is consumed and is available for a price: Consume till MUx = Pricex

Optimization Rule 3: Law of Equi Marginal Utility or Law of Substitution : The law states that the consumer will spend his income on different goods in such a way that marginal utility of each good is proportional to it’s price ie. when more than one good is consumed and the goods’ prices are different: Consume till MUx/Px = MUy/Py = MUz/Pz

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.

The rule is to carry on allocating additional rupees to the commodity until the marginal utility derived from the last additional rupee is the same irrespective of the commodity that it is spent on, and the income is exhausted.

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 p. X. Let MUY and p. Y 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/p. X.

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

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.

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.

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

A consumer surplus occurs when the consumer is willing to pay more for a given product than the current market price. Consumers always like to feel like they are getting a good deal on the goods and services they buy and consumer surplus is simply an economic measure of this satisfaction. For example, assume a consumer goes out shopping for a CD player and he or she is willing to spend $250. When this individual finds that the player is on sale for $150, economists would say that this person has a consumer surplus of $100. Consumers Surplus

Glasses of Total milk utility consumed per week Marginal Utility Consumer ’s surplus on each glass if milk costs 0. 30 per glass 1 3. 00 2. 70 2 4. 5 1. 2 3 5. 5 1 . 7 4 6. 3 . 8 . 5 5 6. 9 . 6 . 3 6 7. 4 . 5 . 2 7 7. 8 . 4 . 1 8 8. 1 . 3 0 9 8. 35 . 25 10 8. 55 . 2

Consumer’s Surplus for an Individual Price of milk [£ per glass] 3. 00 2. 00 Market price 1. 00 0. 30 1 2 3 4 5 6 7 8 Glasses of milk consumed per week 9 10

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.

The Utility Theory of Demand Marginal utility theory distinguishes between total utility that each consumer gets from consumption of all units of some product and marginal utility each consumer obtains from consumption of one more unit of the product. the the ◦ 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.

Indifference Curve – Ordinal Approach An indifference curve shows combinations of products that yield the same satisfaction to the consumer. The amount of Y that the individual would be willing to give up for X is called the marginal rate of substitution i. e. slope of the indifference curve.

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

Bundles Conferring Equal Satisfaction Quantity of clothing per week 35 a 30 25 20 g b 15 c d 10 h 5 5 10 e f T 15 20 Quantity of food 25 30 35 Ranking commodity bundles : g is preferred to b & c; b& c is preferred to h

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.

Indifference Curves Properties of Indifference curves: - Slope downward: Whenever quantity of one good increases, quantity of the other good decreases. - Convex to the origin and are based on the principle of diminishing marginal rate of substitution. Absolute value of MRS has to decrease as the consumer moves away from the origin on the X - axis - Non intersecting : If two indifference curves crossed, it would mean that one of them refers to a higher level of satisfaction than the other at one side of the intersection and to a lower level of satisfaction at the other side of the intersection.

Quantity of food per week An Indifference Map I 5 I 4 I 3 I 1 0 Quantity of food per week I 2

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 everhigher utility levels.

Shapes of Indifference Curves I 2 Perfect Complements Left hand gloves Perfect Substitutes I 2 I 1 0 0 [i]. Packs of green pins [ii]. Right hand gloves

Perfect substitutes are having a constant rate of substitution at all levels of consumption. Complements are consumed in fixed proportions.

Shapes of Indifference Curves A good that confers a negative utility after some level of consumption An absolute necessity All other goods I 2 A good that confers a negative utility after some level of consumption I 2 I 1 0 0 w [iv]. Water I 1 [v]. Food The marginal rate of substitution for an absolute necessity approaches infinity as consumption falls towards the amount that is absolutely necessary. f 0 0

Opportunity Set Defined by Budget Constraint. 6 x + 3 y = 60 Given Px = 6 and Py = 3 • If the consumer spends all his income only on X, he can purchase 10 units of X, while if he spends all his income on Y, he can purchase 20 units of Y. Combination of income spent on X and Y gives the Budget Line • A change in income, with no change in prices, will lead to a parallel shift in the budget line. • Slope of the budget line changes only when the relative prices change other things remaining the same -Px/Py is the Slope

Consumer Equilibrium ◦ The goal of the consumer is to buy the affordable quantities of goods that make the consumer as well off as possible. ◦ The consumer’s preference map describe the way a consumer values different combinations of goods. ◦ The consumer’s budget and the prices of the goods limit the consumer’s choices.

Figure shows consumer equilibrium. Tina’s indifference curves describe her preferences. Tina’s budget line describes the limits to what she can afford. Tina’s best affordable point is C. At that point, she is on her budget line and also on the highest attainable indifference curve.

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

Budget Line – shows all those combinations of the goods that are just obtainable given Jane’s income and the prices of the products that she buys. Slope of the budget line

Quantity of clothing per week The Equilibrium of a Consumer 30 a b 25 c 20 E 15 10 I 5 d I 4 5 e f 5 10 15 20 Quantity of food per week 25 30 I 3 I 2 I 1 35

Satisfaction is maximized at the point where an indifference curve is tangent to a budget line. At that point, the slope of the indiffference curvewhich measures the consumer’s marginal rate of substitution – is equal to the slope of the budget line – which measures the opportunity cost of one good in terms of the other as determined by market prices.

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 I 4 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 I 3 and thus to a lower level of satisfaction.

Tina can consume the same quantity of water at point J but less gum. She prefers C to J. Point J is equally preferred to points F and H, which Tina can also afford. Points on the budget line between F and H are preferred to F and H. And of all those points, C is the best affordable point for Tina.

Deriving the Demand Curve ◦ To derive Tina’s demand curve for bottled water: Change the price of water Shift the budget line Work out the new best affordable point

Figure A 11. 4 shows how to derive Tina’s demand curve. When the price of water is $1 a bottle, Tina’s best affordable point is C in part (a) and at point A on her demand curve in part (b). When the price of water is 50 cents a bottle, Tina’s best affordable point is K in part (a) and at point B on her demand curve in part (b).

Tina’s demand curve in part (b) passes through points A and B.

An Income-consumption Line Quantity of clothing per week Income-consumption line E 3 E 2 E 1 A change in consumer’s income shifts the budget line parallel to itself, outwards when I income rises and inwards when income falls 3 I 2 I 1 0 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 E 1 to E 2 to E 3. · The black income-consumption line joins all these points of equilibrium.

An equal proportionate change in all money prices, with money income held constant, shifts the budget line parallel to itself, towards the origin when prices rise and away from the origin when prices fall.

Homogenity condition Multiplying money income by some constant, λ, and simultaneously multiplying all money prices by λ, leaves the budget line unaffected and hence leaves consumer purchases uaffected.

Changes in the slope of the Budget Line A change in relative prices: At a given price of clothing, Karen has an equilibrium consumption position for each possible price of food. Connecting these positions traces out a price-consumption line. As price of food falls, Karen buys more food. So, as relative prices of food and cloting change, the relative quantities of food and clothing change purchased also change.

The Price-consumption Line Quantity of clothing per week a Price-consumption line E 1 E 2 E 3 I 2 I 1 b c Quantity of food per week d

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 E 1, to E 2 to E 3. · The black price-consumption line joins all such equilibrium points.

Value of all other goods [£ per month] Derivation of an Individual’s Demand Curve E 1 E 0 I 0 0 Price of petrol [£ per month] Price-consumption line E 2 60 120 267 I 1 I 2 400 800 [i] Petrol [litres per month] x 0. 75 y 0. 50 z 0. 25 0 Demand curve 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 E 0, E 1, and E 2. · 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 E 0, E 1 and E 2 in part (i).

The Income and Substitution Effects a Good Y a 1 A fall in the price of Good X leads to increase in consumption of Good X due to the substitution effect and the income effect E 0 E 1 Substi Income tution effect 0 q 1 I 1 b q 2 j 1 Quantity of Good X

The substitution effect is defined by sliding the budget line around a fixed indifference curve; the income effect is defined by a parallel shift of the budget line.

Negative income effect only partially offsets the substitution effect , thus quantity demanded increases as a result of the price decrease, though not as much as for a normal good.

The negative income effect outweighs the substitution effect and thus leads to a positively sloped demand curve.

Equivalent variation: It is calcualted by shifting outwards the original budget line parallel to itself until it just touches the new indifference curve achieved after a price fall of one good. Compensating variation: It is the amount of income thathas to be taken away from the consumer following a price fall of one good in order to return the consumer to the initial indifference curve , thus leaving him/her just as well off as before.

The Income and Substitution Effects