Essay on the Ordinal Utility Theory | Theories | Microeconomics

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Essay on the Ordinal Utility Theory

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Essay Contents:

1. Essay on the Advances Made by the Ordinal Utility Theory
2. Essay on the Consumer’s Preferences
3. Essay on the Consumer’s Financial Constraints
4. Essay on the Equilibrium of Consumer
5. Essay on the Applications of Ordinal Utility Theory
6. Essay on the Limitations of Ordinal Utility Theory

Essay # 1. Advances Made by the Ordinal Utility Theory:

This theory is designed to overcome the several limitations of the cardinal utility theory. A generalized utility function is adopted, and money is dropped from the utility function. The theory is free of the cramping reliance on the constancy of marginal utility of money, independence of marginal utility of goods and diminishing marginal utility which characterizes the cardinal utility theory. Thus the ordinal utility theory is far more general than the cardinal utility theory.

The most significant outcome of the ordinal theory is the revival of an older finding relating to consumer demand. These states – If more of a good is demanded at a higher income, less of it will be demanded at a higher price, cet. par. Thus, the income effect and price effect on demand are brought together in a single explanation.

This integration helps the theory to explain the phenomenon of inferior and Giffen goods which evades the grasp of cardinal utility theory. Unlike the cardinal utility theory, cross price effects are accommodated by the ordinal utility theory. The ordinal utility theory achieves this wider range of explanation with weaker assumptions.

Broadly speaking, it is enough for the theory if:

(a) The consumer consistently ranks his satisfaction in the order of more, less or equal to,

(b) If he is insatiable, and

(c) His preferences exhibit a convexity.

The last implies that the consumer prefers an average of any two equally preferred combinations of goods to either combination. To these crucial assumptions are added a few simplifying assumptions and the analysis is based on simple graphical apparatus, although differential calculus can be used with more general results.

For convenience, we will develop the model of consumer behaviour based on the ordinal utility theory on the assumption that there are only two goods: apples (x) and nuts (y). We will further assume that these goods are perfectly divisible, so that every point on the graph shown in Fig. 5.1 represents some combination of apples and nuts. And all combinations of apples and nuts are represented in the graph in Fig. 5.1. Thus Fig. 5.1 can be used to study the consumer’s choice.

Essay # 2. Consumer’s Preferences:

The Consumer’s Satisfaction and Preferences:

The assumptions about the consumer’s preferences are sometimes introduced as axioms. However, these assumptions are not as self-evident as the term would imply, and so they bear some explanation by reference to the satisfaction of the consumer. This is the approach we adopt here.

The assumptions made are as follows:

1. The consumer’s preferences reflect the satisfaction he gets from different combinations of goods.

2. The consumer can compare the satisfaction from different combinations and rank them in the order of more, less or equal.

3. The consumer’s ranking is complete and transitive.

4. The consumer’s utility is a continuous differentiable function of his consumption.

5. The time period of analysis is long enough to satisfy the taste for variety in consumption, without being long enough to allow for a shift in preferences or tastes.

6. The consumer is insatiable, within the range of analysis.

7. The consumer’s preferences are convex.

Let us now discuss these assumptions in some detail.

Assumptions:

1. The Consumer’s Preferences Reflect the Satisfaction He gets:

This implies rational behaviour. Given any two combinations of goods, A and B, the consumer will prefer A to B if A gives him more satisfaction and prefer B to A, if B gives him more satisfaction. If A and B give him equal satisfaction he reports indifference.

The relation between satisfaction and preferences is illustrated in Fig. 5.2. Here we have drawn an imaginary third dimension U in order to measure the consumer’s satisfaction. We can see that the satisfaction, derived from combination A is more than the satisfaction derived from B. Hence the consumer will prefer A to B.

2. The Consumer can Compare Satisfaction from Goods and Rank the Satisfaction He gets in the Order of More, Less or Equal to:

This assumes an ‘ordinal’ measurement of satisfaction. That is to say, the consumer is able to rank his satisfaction from different combinations. Unlike in cardinal theory, he is not required to report his satisfaction in numbers, because there is no inter-subjectively meaningful standard for measuring utility. For ordinal utility theory, it is enough that the consumer can rank his satisfaction.

3. The Consumer’s Ranking is Complete and Transitive:

This implies firstly, that all combinations in Figs. 5.2 and 5.1 are ranked. That is to say, given any two commodity combinations A and B, the consumer can ‘look up’ the third dimension U (in Fig. 5.2), and report whether he is getting more, equal or less satisfaction from A compared to B. There are no ‘blind spots’ in the consumer’s preferences. This is called completeness.

Secondly, this assumption requires transitivity in ranking. Thus, if the consumer ranks two apples higher than one, and three nuts higher than two apples, he must thereby rank three nuts higher than one apple.

Algebraically, this requires that:

U_A > U_B, U_B > U_C Þ U_A > U_C

4. The Consumer’s Satisfaction is a Continuous, Differentiable Function of His Consumption:

Algebraically,

U = f (x, y)

where f_x, and f_y are defined, continuous and differentiable.

The above states that utility is a function of the quantities of apples (x) and nuts (y) consumed. When we assert that utility is a function of x and y, we are stating that any given combination of x and y gives only one level of satisfaction, and not more. This seems to be fairly plausible.

5. The Time Period is Long Enough to Allow for Variety in Consumption, but is Short Enough to Ensure Stability of Tastes and Preferences:

Consumption takes time. And often, the desire for variety is satisfied sequentially over time. For instance, no one would like to have tea and coffee simul­taneously. However, over the day, some may prefer to have two cups of coffee and four cups of tea, or conversely. Thus the desire for variety will not manifest itself unless the period of analysis is long enough.

The problem with time is that preferences and tastes also change over time. This makes it difficult to decide whether the evening cup of coffee should be treated as a change in taste from the morning preference for tea, or whether it should be seen as a sign of the desire for variety. This problem becomes more serious if consumption takes a longer period.

For instance, the pleasure of a freshly painted house is savoured for a few years. If, after a few years, a consumer repaints his house in a different colour, is he satisfying his taste for variety sequentially, or have his tastes changed? A very fine line of distinction between the two possibilities is drawn by our assumption.

6. The Consumer is Insatiable within the Range of Analysis:

Non-satiety applies to individual goods as well as their combinations. It implies that a larger quantity of a good (or goods) cet. par., will give greater satisfaction. Hence, the consumer always prefers more to less, within the range of analysis.

Non-satiety, as applied to individual goods, implies positive marginal utilities. That is, an increase in the consumption of any one good, cet. par. increases the satisfaction of the consumer. Ceteris paribus, in this context means that the quantities consumed of other goods remain constant. Positive marginal utilities establish a trade-off between the two goods in equal-satisfaction or indifference sets.

An equal-satisfaction set is the set of all combinations of the two goods that yield equal satisfaction. Consider any two equally satisfying combinations B and C. Due to positive marginal utilities, the following relation obtains – If B has more apples than C, it must have less nuts than C. This is because, more apples add to satisfaction when marginal utilities are positive. And so, this additional satisfaction must be reduced by subtracting nuts until the two combinations give equal satisfaction. Thus a trade-off between the two goods is established between equally satisfying combinations by positive marginal utilities.

Indifference Curves:

The set of all equally satisfying combinations can be described by an equal-satisfaction or indifference curve. This is drawn in Fig. 5.3. It may be seen that the indifference curve slopes down to the right. This reflects the trade-off between the two goods among equally satisfying combinations. We have proved that this trade-off results from positive marginal utilities of goods, that is, from the assumption of non-satiety.

Marginal Rate of Substitution:

Non-satiety has other important implications for indifference curves. For the present, we note that it establishes a trade-off between goods on an indifference curve. A measure of the rate at which one good is traded off for another at any point on the indifference curve is called the marginal rate of substitution (MRS). It may be defined as the rate of substitution of the increasing good by the decreasing good at any point on the indifference curve. It is measured by the slope of the indifference curve at the point.

This is shown in Fig. 5.4. It can be seen that the slope of the indifference curve, tan ɸ, measures the ratio – (Δy/Δx), when Δx is very small. This ratio represents the marginal rate of substitution. It can be shown that the marginal rate of substitution is equal to the ratio of marginal utilities. Algebraically,

The preferences of the consumer are convex, which is to say that indifference curves are convex from below, or that the marginal rate of substitution is diminishing.

Preference for Averages:

Convexity of preferences implies that any average of two equally satisfying combinations of goods gives more satisfaction than either combination. Graphically, this amounts to assuming that indifference curves are convex from below or the MRS is diminishing. This is illustrated in Fig. 5.5.

In Fig. 5.5, A and B are equally satisfying combinations lying on IC₁. The line AB represents all possible weighted averages of the two combinations A and B. It can be seen that the line AB lies above the indifference curve IC₁ because the indifference curve is convex from below. Since AB lies above the IC₁, all points on it must give more satisfaction than IC₁. This is because, on any point, AB has more of at least one good (e.g. y₁ > y₀). And since the marginal, utility of that good is positive the satisfaction on AB must be more than on IC₁. Hence all averages of A and B give more satisfaction than either A or B which lie on IC₁. Thus averages are preferred to either equally satisfying combination. This is called the convexity of preferences.

Imperfect Substitutes:

There is another way of explaining the convexity of indifference curves. This is illustrated in Fig. 5.6. Three types of indifference curves are drawn here.

Let us first consider U⁰ which is a straight line indifference curve. On this indifference curve, at every point, the consumer gives up two nuts to compensate for the extra satisfaction generated by an extra apple. Clearly, he seems to think that two nuts are a perfect substitute for; one apple. Thus, any straight line indifference curve which slopes down to the right illustrates the case of perfect substitutes.

Now consider the right angled indifference curve U¹. Here, at point J, the increase of either nuts or apples does not increase satisfaction. Thus J represents a jointly consumed combination. In such cases, only the increase of both goods increases satisfaction and an isolated increase are wasted. Typical examples are given by pairs such as shirts and buttons, and so on. Thus right angled indifference curves represent the case of strictly jointly consumed goods.

We see that the convex indifference curve U², represents a case which is intermediate to the right angled indifference curve U¹ and the straight line indifference curve U⁰. Hence, it describes a case intermediate to perfect substitution and strict jointness of consumption. Thus we may infer that indifference curves that are convex from below reflect the imperfect substitutability or the incomplete jointness of consumption of the two goods.

Diminishing Marginal Rate of Substitution:

Convexity of the indifference curve can be alternatively described in terms of its slope. It can be seen from Fig. 5.7, that the slope of the indifference curve decreases as x increases if the curve is convex from below (tan ɸ₂ < tan ɸ₁). This means that the marginal rate of substitution decreases, as we have more of the increasing good (x). Hence diminishing marginal rate of substitution (DMRS), is another name for the convexity of indifference curves.

Since MRS is equal to the ratio of marginal utilities, what DMRS means is that the ratio of marginal utilities f_x/f_y decreases as x increases.

DMRS obtains when the following condition is fulfilled by the marginal utilities:

The parenthesized term must be negative for DMRS, since, the marginal utilities (f_y) are positive. It must be noted that the condition for DMRS does not require diminishing marginal utility (f_xx, f_yy < 0), nor is diminishing marginal utility sufficient for DMRS. The condition [2] that characterizes DMRS is important.

Indifference Curves:

Our assumptions have led us to indifference curves. Indifference curves constitute the principal tool of ordinal utility theory. Their shape and properties reflect the assumptions about the consumer’s tastes and preferences. 

Properties:

1. Equally Satisfying Combinations:

An indifference curve is a line on which all the points represent equally satisfying combinations of two goods.

2. Slopes Down to Right:

An indifference curve slopes down to the right because of positive marginal utilities of individual goods resulting from the assumption of non-satiety.

3. Convex from Below:

An indifference curve is convex from below, because we assume—(a) convexity of preferences (b) imperfect substitutability or incomplete jointness in the consumption of goods and (c) condition [2].

4. Higher Curve gives More Satisfaction:

A higher indifference curve gives greater satisfaction. This again follows from the principle of non-satiety. This is because a higher indifference curve has more of one or both goods than the lower curve, at some points. Since more goods yield more satisfaction by the principle of non-satiety, the higher indifference curve must give greater satisfaction.

5. Two ICs cannot Cross:

Two indifference curves cannot cross.

This last property is discussed below:

This can be shown by the implausibility of the converse. If two indifference curves cross, as in Fig. 5.8, one must be higher than the other before the point of intersection A, and below the other after this point. So, before A, it must give greater satisfaction, while after A, it must give less satisfaction than the other, curve. But this is a contradiction, since the satisfaction on each curve is constant by assumption.

Another proof runs as follows. By assumption, any combination of goods can give only one level of satis­faction. Now consider combination A which lies on both indifference curves. Since the two indifference curves are different, they give different levels of satisfaction. There­fore A, which lies on both curves, must give two different levels of satisfaction. This is again a contradiction.

Thus, two indifference curves cannot cross. A corollary of the last argument, is that, if two indifference curves do have one point in common, they must coincide at all points. That is, they cannot be different. The collection of all ICs of a consumer is called his ‘indifference curve map’ and it reflects his tastes.

Essay # 3. The Consumer’s Financial Constraints:

The financial constraints of the consumer are represented by his budget and the market prices. We make two simplifying assumptions about the consumer’s budget.

Assumptions:

1. The consumer has a consumption budget (B) that may be represented as a constant fraction of his income (Y). For convenience, we assume that the consumption budget accounts for the whole of consumer’s income and is synonymous with it.

2. The consumer spends his entire budget on current consumption, in our case, on apples and nuts. Thus

B = p_xx + p_yy                             …[3]

Equation [3] is called the budget constraint. It shows that the consumer spends his entire budget on current consumption. The budget constraint implies that the consumer cannot maximize his satisfaction without exhausting his budget. This is once again the principle of non-satiety, but this time in a financial guise.

The Budget Line:

The budget constraint can be graphically described after being rewritten as eqn. [3a]. In its new form, it shows the quantity purchasable of one good y as a function of the quantity purchased of the other x. Thus,

In this form, the budget constraint can be shown graphically as in Fig. 5.9.

If the entire budget is spent on nuts, at the prevailing price, B/p_y can be purchased. This is given by OC. Similarly, if the entire budget is spent on apples, at prevailing price of apples, B/p_x can be purchased. This is measured by OD. The straight line CD joining these two quantities B/p_x, B/p_y, is the budget line. Every point on the budget line represents some combination of goods that can be purchased by exhausting the budget of the consumer at the prevailing prices.

Real Income:

It can be seen that the height of the budget line represents the consumer’s real purchasing power or income. If the consumer’s budget rises in a given price situation, the budget line rises. This is because, B/p_x and B/p_y rise proportionately when B increases. However if the prices also change in the same proportion as the budget, the budget line remains where it was. Thus the budget line is homogenous to degree zero in the prices and the consumer’s budget. This can also be checked from eqn. [3a].

Price Ratio:

The slope of the budget line, tan ɸ gives the price ratio. Specifically, the slope, tan ɸ, is equal to the ratio of the price of x to the price of y (tan ɸ = p_x/p_y). Since the price ratio of the two goods is equal to the slope of the budget line, it is also called the price line at times.

If good x (apples in our example) becomes cheaper, the slope of the budget line decreases, as shown in Fig. 5.10. The slope declines because the same budget can purchase more apples when they are cheaper.

Available Combinations:

Combinations of goods that lie above the budget line (e.g. G), are beyond the reach of the consumer. He cannot purchase such combinations in the given price-budget situation. In any price-budget situation, all the alternative combinations that the consumer can purchase by spending his entire budget are given by the budget line. From these alternative combinations, the consumer must choose an equilibrium combination.

Essay # 4. Equilibrium of the Consumer:

The equilibrium combination is one that maximises the consumer’s satisfaction.

Since the consumer is assumed to be insatiable, he aims to maximize his satisfaction. His desire for ever greater satisfaction drives him up the indifference curve map (see Fig. 5.11), since higher indifference curves give more satisfaction than lower curves. But this movement up the indifference curve map is restrained by his budget constraint. Combinations above the constraint are beyond his reach.

Hence the consumer chooses that combination on the budget line at which the highest indifference curve touches it. This combination of goods E maximizes the consumer’s satisfaction given his constraints. Hence, this combination represents his equilibrium demand for the two goods.

Characteristics of Consumer Equilibrium:

Usually, in equilibrium, the consumer demands some quantities of both goods. Such equilibrium is called an interior solution. In contrast to the interior solution, there is the less usual case where one good is completely excluded from the consumer’s demand. Such a case is called the corner solution. The characteristics of consumer equilibrium differ between these two cases.

Let us examine them sequentially:

1. Interior Solution – Characteristics:

This is the usual case where the consumer demands some quantity of each good in equilibrium. In such cases, the consumer’s equilibrium is established at the point at which the budget line is tangential to some indifference curve, and the indifference curve is convex from below.

Proof:

a. Tangency:

Suppose that the indifference curves are convex from below. In such a case, points on the budget line where it cuts some indifference curve (e.g. Q in Fig. 5.12), cannot provide the maximum satisfaction. This is because, if the budget line cuts some indifference curve U₁ at Q, it has to be higher than U₁, at some other point. At these higher points, the satisfaction will be greater than U₁, because higher indifference curves will pass through them. Hence, Q cannot provide the maximum satisfaction. The maximum satisfaction can only be provided by that point at which the budget line is tangential to some indifference curve, as at E.

b. Convexity:

At the point of tangency, the indifference curves must be convex from below to ensure a maximum. The importance of convexity at the point of tangency is illustrated by Fig. 5.13. Here at Q, the point of tangency, the indifference curve U₁ is concave from below. It can easily be seen that indifference curves higher than U₁, touch the budget line elsewhere (e.g. U₂ and U₃). Hence if at the point of tangency, the indifference curve is concave, the point cannot represent the maximum possible satisfaction, given the consumer’s constraints.

In contrast, at E, where the indifference curve is convex from below, the satisfaction is maximum. Since U₃ is convex from below at E, no higher indifference curve can be found touching the budget line. Hence, if the indifference curve is convex at the point of tangency with the budget line, it represents a constrained maximum.

Implications:

In equilibrium, the MRS, i.e. the ratio of the marginal utilities of the two goods, equals their price ratio. This is because, when the budget line is tangential to an indifference curve, their slopes are identical. We already know that the slope of the indifference curve is equal to the ratio of marginal utilities (MRS), and the slope of the budget line is equal to the price ratio. Hence, in equilibrium, the price ratio equals the ratio of marginal utilities. Algebraically,

The above property implies the law of equimarginal utility, which states that the marginal utility per rupee spent, is the same for all goods. This is seen by simply rearranging and rewriting the equation as f_x/p_x = f_y/p_y. The properties of interior solutions are also developed in the mathematical appendix through the use of differential calculus. However, differential calculus cannot so easily describe the properties of corner solutions.

2. Corner Solutions – Characteristics:

A corner solution is said to obtain when one of the goods is wholly excluded from the consumer’s demand. Such a situation can arise when indifference curves are convex from below. This possibility is illustrated by C, Fig. 5.14(a). But if the indifference curves are wholly concave from below, a corner solution is inevitable. One good will always be excluded from the consumer’s demand. This is illustrated by C and E, Fig. 5.14(b).

Significance:

What is the significance of a concave indifference curve? Concavity from below indicates that the average of any two equally satisfying combinations will give less satisfaction than either. Thus, the consumer may report equal satisfaction from a tube of Colgate toothpaste or from a tube of Vajradanti, but may find any weighted average of the two less satisfying than either. In such a case, the indifference curve drawn for the two brands of toothpaste will be concave from below, as in Fig. 5.14(b). A concave indifference curve is one of the two possibilities, if the consumer’s demand wholly excludes one good.

The chief characteristic of a corner solution is that the budget line is no longer tangential to the indifference curve if it is concave. And if the indifference curve is convex as in Fig. 5.14(a), its slope is indeterminate at the point of tangency. As a result, the law of equimarginal utility can no longer be derived from the equilibrium conditions. Corner solutions are inconvenient to handle.

Essay # 5. Applications of the Ordinal Utility Theory:

Choice between Income and Leisure:

The time of a casual labourer is a resource that he can devote to leisure (L) or earning an income (Y). His access to income depends upon the going wage rate (w). The higher the wage rate, the greater his access to income. We can represent this as in Fig. 5.27. Here Y₁ and Y₂ represent the maximum income which the labourer can earn at two different wage rates, were he to spend all his days working. The wage rates are measured by,

The labourer enjoys consuming the goods his income fetches, as well as his leisure. He has however, to choose an optimum combination of leisure and income. The leisure chosen by him will determine his supply of labour (S₁ = 365 – L), and his income at the going wage rate. The optimum combination of leisure and income chosen by the labourer at any wage rate is shown in Fig. 5.28. Here, at the wage rate ɸ, L_d is the leisure demanded, and the income demanded is Y_d. The supply of labour is 365 – L_d.

Effects of Wage Increase:

Suppose that minimum wage legislation is enacted, so that the wage rate increases from tan ɸ to tan τ. How will the higher wage affect the demand for leisure (L_d) of the labourer and his supply of labour (S₁)? Will the labourer take more ‘days off or less, now that the wage rate is higher?

Figures 5.29 and 5.30 show that both consequences are possible. Figure 5.29 shows that labourer A demands less leisure at a higher wage rate. Hence, he supplies more labour at the higher wage rate. In contrast, labourer B prefers more leisure at a higher wage rate. Hence, he supplies fewer days of labour at a higher wage rate.

Price Vs. Income Subsidies:

Suppose a consumer is in equilibrium (x₁, y₁) in a price-budget situation described by B₁. If the price of x goes up, the budget line shrinks to B₂. The consumer is brought to a lower level of satisfaction. Now, if the government wishes to restore the consumer to the old level of satisfaction U₁, it has two ways of doing so. It can subsidize the sellers of x, so that they charge the old low price. This is called a price subsidy. Alternatively, it can give an income subsidy to the consumers. Which mode of compensation by the government is to be preferred?

Income Subsidy Cheaper:

It can be shown that a compensating income subsidy is less expensive than a compensating price subsidy. This is seen from Fig. 5.31. In Fig. 5.31, the price subsidy restores the old command over the goods x₁,y₁.

In contrast, the income subsidy (B₂  → B₃) restores the old level of satisfaction U_1, although the old combination of goods x₁, y₁ is still too expensive for the consumer. Thus an income subsidy is less expensive to the government than a price subsidy, although both have the same effect on the consumer’s welfare.

Reasons:

Why should this be so? Graphically, it is because price subsidies have to ‘reach round’ the bulge of convex ICs, whereas income subsidies do not. The convexity of ICs arises from the fact that consumers prefer an average of both, to either of equally preferred combinations. Price subsidies stress only one good, and so go against the taste for averages.

Income subsidies ease the way to both combinations, and so less is spent by way of income subsidies to secure the same welfare. A corollary of the above argument is that if the same amounts are spent on price and income subsidies, the latter raise welfare by more.

Consumer’s Surplus and Indifference Curves:

Once we drop the assumption of constant marginal utility of money, consumer’s surplus can no more be measured by the area between the individual demand curve and the price line. Hicks therefore proposes an alternative mode of measurement.

Measurement by CVI:

The consumer’s satisfaction from purchasing a good is greater than when he is not purchasing it. If we can estimate the compensating variation of income which reduces the consumer’s satisfaction to the level when he is not purchasing a good, it can serve as a measure of the Consumer’s Surplus.

Following up on this idea, Hicks suggested that:

Consumer’s surplus can be measured by a compensating variation in income “whose loss would just offset the fall in price [from exit price] and leave the consumer no worse off than before”.

We can explain this as follows – Suppose that the price of the good x is so high as to force the consumer to just leave the market for good x. At this exit price CH, the consumer gets some satisfaction U₁ (see Fig. 5.32), because he consumes other goods although he does not purchase the good x. Now, if the price of the good x is cut to OD, the consumer purchases some quantity of the good x and his level of satisfaction rises from U₁ to U₂.

The difference between U₂ and U₁ is his surplus satisfaction. We can measure this surplus satisfaction by the compensating variation of income which returns the consumer from U₂ to U₁. This compensating variation of income (CD → BB) which restores the consumer’s satisfaction to the level prevailing at the exit price is the Hicksian measure of Consumer’s Surplus.

The Hicksian consumer’s surplus, it can be seen, is no longer a sum of utility. It is however, a ‘perfectly well defined, measurable concept’.

Graphical Illustration:

The significance of the Hicksian measure may be demonstrated through the indifference curve apparatus. This is done in Fig. 5.32. Here, money income is measured on the Y axis. It represents the command over all goods other than x. The prices of all these other goods are fixed.

CD represents the situation at the current price of x. However, we begin from the exit price of x, where it is not purchased. This is denoted by CH, which gives a corner solution, excluding x from the consumer demand. At CH, the consumer’s satisfaction level is U₁.

The consumer’s satisfaction rises to U₂, when the price is reduced. This is shown by the consumer’s equilibrium on CD. Hicks’ method of measurement of the consumer’s surplus involves a compensating variation at current prices, lowering the budget line to BB. At BB, the consumer’s satisfaction is the same (U₁) as when he had not purchased x at all. Thus, at income B, the consumer is as satisfied as he was before he entered the market for x, due to a fall in its price. CB therefore measures the consumer’s surplus.

Essay # 6. Limitations of the Ordinal Utility Theory:

The chief defect of the ordinal utility theory is that it is based on psychological attributes which cannot be directly observed. Thus the characteristics of the individual’s utility surface cannot be directly observed. This is considered to be a drawback by economists who believe that theories must be cast in terms that are all directly observable.

To overcome this limitation, Samuelson developed the Theory of revealed preference which is entirely based on observable behaviour of a consumer, and some assumptions about his rationality. When confronted with this theory, Hicks admitted the limitations of the utility approach to consumer demand.

Apart from this, the ordinal utility theory has to make numerous assumptions for mathematical and logical convenience, which may not be justified. These assumptions ensure the continuity and smoothness of the utility function, which is necessary for determinate results. Similarly, in the interests of determinate results, the significance of corner solutions is underplayed. However, these limitations may be regarded as the necessary costs of simplification. They do not detract from the general appeal of the model.