2.1.1. Cardinal Utility Analysis

Cardinal utility analysis assumes that level of utility can be expressed in numbers. For example, we can measure the utility derived from a shirt and say, this shirt gives me 50 units of utility.

Cardinal utility analysis is based on the idea that utility, or the satisfaction a consumer derives from a good or service, can be quantified numerically. For example, if someone says a shirt gives them 50 units of utility, they're quantifying their satisfaction from that shirt. This approach contrasts with ordinal utility analysis, where utility is ranked but not assigned a specific numerical value.

Imagine if you rated your favorite foods on a scale from 1 to 100, where chocolate cake might score 90 for you, while broccoli might score only 30. This way of ranking satisfaction is like using cardinal utility, but you could also simply say you prefer chocolate cake to broccoli without giving them scores, which aligns with ordinal utility.

Total utility of a fixed quantity of a commodity (TU) is the total satisfaction derived from consuming the given amount of some commodity x.

Total utility (TU) refers to the overall satisfaction a consumer experiences from consuming a specific quantity of a good. As consumption increases, total utility generally rises; more of a commodity often leads to greater satisfaction. For example, if eating ice cream makes you happy, the more ice cream you eat, the more happy you will feel until you reach a point of saturation.

Think of a video game. The more levels you complete, the more fun and satisfaction you derive from it. If completing three levels gives you an excitement score of 30, and completing four levels boosts that to 40, then your total utility has increased as you consume more content.

Marginal utility (MU) is the change in total utility due to consumption of one additional unit of a commodity. For example, suppose 4 bananas give us 28 units of total utility and 5 bananas give us 30 units of total utility. Clearly, consumption of the 5th banana has caused total utility to increase by 2 units (30 units minus 28 units). Therefore, marginal utility of the 5th banana is 2 units.

Marginal utility measures the satisfaction gained from consuming one more unit of a good. In the example given, when a consumer eats the 5th banana, they derive an additional 2 units of satisfaction compared to if they stopped at 4 bananas. The formula for calculating marginal utility is the difference in total utility as additional units are consumed, demonstrating the incremental changes in satisfaction.

Imagine you are at a buffet. The first slice of pizza might bring you immense satisfaction (let's say 10 units!), but by the time you reach your fifth slice, the extra joy you get might be only 2 units. Here, the marginal utility diminishes for each additional slice you consume.

In general, MU = TU – TU, where subscript n refers to the nth unit of the commodity. This simply means that TU derived from consuming n units of bananas is the sum total of marginal utility of first banana (MU1), marginal utility of second banana (MU2), and so on, until the marginal utility of the nth unit.

Total utility can be seen as the cumulative sum of each unit's marginal utility. To fully understand how much satisfaction one gets from all consumed units, you can add up all marginal utilities. This perspective helps in understanding how the satisfaction received changes with each additional unit consumed.

Think of a sports drink. After finishing one drink, your satisfaction increases by a certain amount, let’s say 10 units, followed by 8 units for the second, and 6 units for the third. To find the total satisfaction from the three drinks, you would sum these: 10 + 8 + 6 = 24 units of total utility.

Usually, it is seen that the marginal utility diminishes with increase in consumption of the commodity. This happens because having obtained some amount of the commodity, the desire of the consumer to have still more of it becomes weaker.

The concept of diminishing marginal utility indicates that as a person consumes more units of a good, the additional satisfaction derived from each successive unit typically decreases. The initial units provide high satisfaction, but as consumption continues, the added satisfaction from each additional unit tends to drop.

Imagine you're at a concert and you've just bought two front-row tickets for an amazing experience. The thrill you feel from the first ticket is enormous, and while the second ticket increased your enjoyment, the thrill for the second one is less intense compared to the first. However, if you purchase a third or fourth ticket, the joy from each further ticket continues to diminish.

Cardinal utility analysis can be used to derive demand curve for a commodity. What is demand and what is demand curve? The quantity of a commodity that a consumer is willing to buy and is able to afford, given prices of goods and income of the consumer, is called demand for that commodity.

The relationship between the price of a commodity and the quantity demanded can be illustrated by a demand curve. As per cardinal utility, when the price of a good falls, the utility derived from consuming additional units increases relative to the price spent, leading consumers to buy more. When applied, we can summarize this relationship graphically, establishing the framework for understanding how demand varies with changing prices.

Consider pizza: if a slice costs $2 and you really enjoy it, you might buy 3 slices. However, if the price drops to$1 per slice, you may now feel compelled to buy 6 slices. The demand curve visually captures this relationship, showing how much of the pizza you buy as prices change.

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