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CHOICE AND UTILITY THEORY Utility is the satisfaction gained by consumers from consumption of goods and services, or it can also be defined as the ability of a good to provide satisfaction to its consumer. According to the theory of utility, consumers use satisfaction level as the basis to make consumption choices and evaluate goods based on satisfaction. Basically, there are two approaches of utility theory analysis namely, the cardinal approach and ordinal approach. Through cardinal approach, it is assumed that utility can be measured with utile as the unit of measurement. For example, eating a piece of durian gives 2 utils, while eating a piece of rambutan will give 1 util. Meanwhile, the ordinal approach, assumes that level of satisfaction cannot be measured. For instance, eating durian gives more satisfaction compared to eating rambutan. In this condition, the measurement unit of satisfaction is not given. The level of satisfaction is determined by means of comparison only. Cardinal Measurement of Utility Cardinal utility theory is a method which assumes that satisfaction can be measured using the unit of ‘util’.
Cardinal utility Utility is said to be measurable in the cardinal sense if not only the utility numbers assigned to bundles but also their differences are meaningful.
Marginal utility analysis assumes in the first place that utility can be measured and the exact measurement can be given by assigning definite numbers such as 1, 2, 2 etc. That is, it is assumed that utility is a quantifiable entity. This means that a person can express the satisfaction derived from the consumption of a commodity in quantitative terms. For instance, eating a piece of cake will give 8 utils, while eating biscuits will only give 4 utils. This reflects that a cake gives two-times the utility compared to biscuits. Utility level is normally reflected by the willingness of a person to pay based on the value of money. The higher the price willing to be paid, the higher the level of satisfaction gained. Ordinal utility theory states that while the utility of a particular good or service cannot be measured using a numerical scale bearing economic meaning in and of itself, pairs of alternative bundles (combinations) of goods can be ordered such that one is considered by an individual to be
Ordinal utility Utility is measurable in the ordinal sense if the utility numbers we assign to objects have no meaning other than to represent the ranking of these goods in terms of a person’s preferences.
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worse than, equal to, or better than the other. This contrasts with cardinal utility theory, which generally treats utility as something whose numerical value is meaningful in its own right. The concept was first introduced by Pareto in 1906. According to the ordinal utility theory, the benefit or satisfaction gained by consumers cannot be measured in quantitative form, but in terms of comparison to the consumption of other goods. The ordinal utility emphasize on ordering/rank bundles of goods. The cardinal utility emphasize on the size of the difference between two bundles of goods. Christopher Pappas When discussing cardinal vs. ordinal, it is helpful to look at what the words mean. The distinguishing factor here is between cardinal and ordinal numbers. Cardinal numbers are 1, 2, 3; ordinal numbers, 1st, 2nd, 3rd. Some crucial differences follow from that. Whereas mathematical operations can be performed on cardinal numbers, they cannot be performed on ordinal numbers. Now, when talking about cardinal utility, it is an attempt to ''measure the utility of various alternatives. When talking about ordinal utility, it is the ''ranking of alternatives.'''' Cardinal utility is, however, an erroneous concept. It is impossible to "measure" utility. People can only say "I prefer A to B", but cannot meaningfully say "I prefer A 2.5 times more than B" or something to that effect.
Total Utility and Marginal Utility There are two basic concepts of utility, namely, total utility and marginal utility. Total Utility (TU) is the total satisfaction gained from a given level of consumption of a good. Marginal utility (MU) is the increase in total utility when consumption increases by 1 unit. Table 3.1 shows the relationship between the consumption of goods with total utility and marginal utility. Observe that total utility for the first unit is 10 utils. When consumption level is increased to 2 units, total utility increases to 22 utils, and so on. As you already know, marginal is addition. The formula for marginal utility is as follows:
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Therefore, marginal utility for the first unit is equivalent to the total utility of that unit. As we can see from Table 4.1, MU for the first unit is 10 utils while for the second unit is 12 or (22 - 10) utils, and so on. Table 3.1: Total Utility and Marginal Utility
When we sum up marginal utility up to 5 consumption levels, we will obtain 38 utiles, that is, equivalent to the total utility of the unit. Figure: 3.1: Total Utility and Marginal Utility
Figure 3.1 is the illustration of total utility and marginal utility derived from Table 3.1. Observe that marginal utility is equivalent to the gradient of total utility at each unit of consumption. Total utility reaches maximum when marginal utility is zero.
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Relationship between “Marginal Utility”, “Total Utility” and “Average Utility” The relation among marginal utility, total utility and average utility can be understood by a careful study of Table 3.2 and Fig. 3.2. It is clear from this table and figure that initially the total utility curve slopes upwards to the right. This indicates that the total utility will rise with consumption of additional units of the commodity. However, the increase in total utility is not constant, but falls steadily. In other words, the total utility rises at a falling rate. This is shown by corresponding downward or negative slope of the marginal utility curve. In the present example, this happens upto 6 units of the commodity.
When the total utility reaches its maximum value, marginal utility becomes zero. Before this point, though marginal utility falls, it always remains positive. In our example, this happens, when the consumer consumes sixth unit of the commodity. It is called the point of satiety. The total utility stops rising at this stage.
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When consumption is expanded beyond the point of satiety, the total utility starts falling because marginal utility turns negative. In the present example, the consumer gets negative marginal utilities of Rs. 2 and Rs. 4, when he decides to consume seventh and eighth units of the commodity respectively.
Fig. 3.2: Relation among MU, TU and AU The relationship between total utility and marginal utility can also be verified mathematically by using the concept of slope. We know that the slope of the total utility curve at each point indicates the marginal utility derived from the corresponding level of consumption. This has been shown in Fig. 3.3.
Fig. 3.3: Marginal Utility though Slope of Total Utility
In Fig. 3.3, four points ‘A’, ‘B’ ‘C’ and ‘D’ are considered on the total utility curve. The slopes at these points are measured by the slopes of the tangents drawn at these points. The slope of the total utility curve at point ‘A’ is AF/EF, while the slope of the total utility curve at point ‘B’ is BH/GH. Since AF/EF > BH/GH, marginal utility for the unit corresponding to point ‘A’ is greater than for the unit corresponding to point ‘B’. Thus, initially, marginal utility falls, as total utility rises at diminishing rate. Further, at maximum point ‘C’ on the total utility curve, the tangent is parallel to X-axis. So, its slope is zero. Therefore, marginal utility is zero, when total utility is maximum. Again, slope of the tangent after point ‘C’ becomes negative (e.g., point ‘D’ in the figure). This shows that marginal utility turns negative, after total utility reaches its maximum point. Unlike marginal utility, average utility is always positive, since it is a ratio of two nonnegative values. So, the graph of average utility always remains above X-axis. When
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average utility attains maximum value, it is equal to marginal utility. Like marginal utility curve, average utility curve is also downward sloping. Law of Diminishing Marginal Utility Utility refers to the amount of satisfaction a person gets from consumption of a certain item. And marginal utility refers to the addition made to total utility; we get after consuming one more unit. An individual's wants are unlimited in number yet each individual's want is satiable. Because of this, the more we have a commodity, the less we want to have more of it. This law state that as the amount consumed of a commodity increases, the utility derived by the consumer from the additional units, i.e marginal utility goes on decreasing. Law of diminishing marginal utility means that the marginal utility obtained from the consumption of additional unit will start to decrease after a certain level of consumption when the amount consumed increases. The law of diminishing marginal utility explains the downward sloping demand curve. Definition According to Marshall, “The additional benefit a person derives from a given increase of his stock of a thing diminishes with every increase in the stock that he already has” Assumptions: All the units of a commodity must be same in all respects The unit of the good must be standard There should be no change in taste during the process of consumption There must be continuity in consumption There should be no change in the price of the substitute goods Explanation: As more and more quantity of a commodity is consumed, the intensity if desire decreases and also the utility derived from the additional unit. Suppose a person eats Bread. And 1st unit of bread gives him maximum satisfaction. When he will eat 2nd bread his total satisfaction would increase. But the utility added
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by 2nd bread (MU) is less than the 1st bread. His Total utility and marginal utility can be put in the form of a following schedule. Table: 3.3: Diminishing Marginal Utility
Plotting the above data on a graph gives Figure: 3.4: Diminishing Marginal Utility
Here, from the MU curve we can see that MU is declinig as consumer consumes more of the commodity. When TU is maximum, MU is Zero. After that, TU starts declining and MU becomes negative.
