    # Cardinal Utility Theory Of Consumer Behaviour Law of diminishing Marginal Utility

Illustration 23

Let us construct a tablet where we have presented the aggregate and marginal utilities derive by a person from ounces of milk consumed per day. Ascertain the marginal utility of utils for 7 ounces consumed a day with the details provided below. Construct the total utility and marginal utility curves that represent the law of diminishing utility.

 Ounces of Milk consumed per day is Q Aggregate Utility in Utils 1 6 2 11 3 15 4 18 5 20 6 21 7 19

Solution

As per the information provided the tablet is structured as follows.

 Ounces of Milk consumed per day is Q Aggregate Utility in Utils Marginal Utility in Utils 1 6 6 2 11 5 3 15 4 4 18 3 5 20 2 6 21 1 7 19 -2

The below diagrams figures out the total and marginal utilities curves, the aggregate utility curves depends on three assumptions. First, as the quantity consumed per period by a consumer hikes his aggregate utility however at a declining rate. This entails that as the consumption per period of a product by the consumer enhances marginal utility diminishes as represented in the diagrams.

Next to it, as will be pragmatic from the diagrams, when the rate of consumption of a product per period enhances to Q4, the aggregate utility of the consumer accomplishes its optimum level. Hence the quantity Q4of the product is termed as contentment quantity.

Next to it the enhancement in the quantity demanded of the good per period by the consumer beyond the contentment level has a bad consequent on his aggregate utility, that is, his aggregate utility decreases if more than Q4 quantity of the commodity is consumed. This entails beyond Q4 marginal utility of the commodity for the consumer becomes negative as will be observed from the second diagram beyond the contentment level Q4. Marginal utility curve MU goes below the X axis depicting it becomes negative beyond quantity Q4 per period of the product consumed.

It is necessary to know how we have drawn the marginal utility curve. As mentioned above, marginal utility is the enhancement in aggregate utility of the consumer caused by the consumption of an extra unit of the product per period. However in terms of calculus marginal utility of a product A is the incline of the aggregate utility function U = f (QA). We directly ascertain the marginal utility of the successive units of the product consumed by measuring the extra utility which a consumer procures from successive units of the product and plotting them against their respective volumes or quantities.

Therefore, we can derive the marginal utility curve by measuring the incline at various points of the aggregate utility curve AU in the prior diagram by sketching tangent at them.

For instance, at the quantity Q1 marginal utility is observed by sketching tangent at point ‘I’ and measuring its inclination which is then plotted against volume or quantity Q1 in the next diagram.

In the second diagram, we measure marginal utility of the product on the Y axis. Similarly, at quantity Q2 marginal utility of the product has been procured by measuring inclination of the aggregate utility curve AU at point ‘J’ and plotting it in the second diagram against the quantity Q2.

It will be observed that from the diagrams that at Q4 of the product consumed the aggregate utility accomplishes at the optimum level ‘L’. Thus, at quantity Q4 the inclination of the aggregate utility curve is zero at this point.

Beyond the quantity Q4 the aggregate utility decreases and marginal utility becomes negative. Therefore, quantity Q4 of the product represents the contentment quantity. Another significant association among aggregate utility and marginal utility is worth make a note of.

At any quantity at a product consumed the aggregate utility is the sum of the marginal utilities. For instance, if marginal utility of the 1st, 2nd and 3rd units of the product consumed are 6, 5 and 4 the aggregate utility procured from these three units of consumption of the product must parity 15 which is the sum of 3 units.

Likewise, in terms of graphs of aggregate utility portrayed in the diagram the aggregate utility of the quantity Q4 of the product consumed is the sum of the marginal utilities of the units of product upto point Q4.

The complete region under the marginal utility curve MU in second diagram upto point Q4 is the total of marginal utilities which should parity the aggregate utility Q4 L in the first diagram.

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