# Link between elasticity and marginal utility

The above is taken from "Economics" 8th Edition by John Sloman, a textbook commonly used at the introductory undergraduate level.

I would like assistance in understanding the bracketed portion - how a decrease in consumption of alternative goods results in a low increase in total utility and thus a small decrease in marginal utility. Thanks.

You may ignore the following picture, "Figure 2". It was uploaded to illustrate something in response to a comment.

• The first sentence in the first bracket refers to opportunity cost. Perhaps you are confused between total utility and marginal utility. May 10, 2017 at 10:53

We can break this into three parts: (1) price elasticity, (2) substitutes, and (3) marginal utility.

Price elasticity measures price sensitivity (how much a change in price affects quantity consumed). In the example in the book, the product is elastic, which means that a decrease in price increases consumption proportionally more than the decrease in price.

Substitutes are any products that can be substituted for another. This is important because a change in price of a product will not only affect it's consumption, but also the consumption of substitute goods. For example, people who want soda have a choice between Coke and Pepsi. Assume that when priced the same, $10$ people by Coke and $10$ people buy Pepsi. The total consumption is $20$. Now, assume that Coke lowers its price while Pepsi keeps the price the same. Some people who once consumed Pepsi will now by Coke, say $5$ people switch to Coke. The total consumption remains the same, $20$, but its distribution is different. It is the case that a drop in price will encourage consumers to purchase Coke who wouldn't normally do so at the initial price. because a price decrease makes the product available to new consumers the total consumption of soda may increase to $25$.

Marginal Utility is the amount by which utility changes with each unit of consumption. The text doesn't seem to say this, but marginal utility is subject to the law of diminishing returns. This means that at a certain point, consuming more of a good makes a person less happy. For example, if I eat 2 cookies, I'm happy. With each cookie I consume, I grow happier in total, however this is happiness increases at a decreasing rate.

Utility is maximized when marginal utility is zero. After this point one loses...experiences disutility.

Essentially, the text is saying that if the price of an elastic good decreases its consumption will increase. The consumption increase comes from (1) "stealing" consumers from other similar products and (2) new consumers that didn't buy the product at the initial price. Since the total consumption increases as did total utility, the increase was small and thus marginal utility decreased. This isn't saying that utility was taken away, its saying the the rate at which utility increased was slower.

• Why do you assume that marginal utility increases over the range 0-4 cookies? The normal assumption is that marginal utility declines (perhaps only very slightly) from even the second unit of a discrete good. May 11, 2017 at 9:25
• Adam's question came to my mind too. I have uploaded a second picture ("Figure 2") which shows how the textbook explained marginal utility in table form. It shows that marginal utility had already started to decrease from the consumption of the second unit of the good. In your answer, you said that "We would say that my utility was maximized by the forth cookie." However, in the textbook, utility is maximised when marginal utility decreases to zero, which contrasts with your example. May 11, 2017 at 12:32
• Another point is this: what if the demand for the good was price inelastic? At the start of your answer, you mentioned that "In the example in the book, the product is elastic, which means that a decrease in price increases consumption." I would assume you meant "increases consumption (i.e. quantity demanded) by a more than proportionate change than the change in price". May 11, 2017 at 12:33
• Since if demand was price inelastic, consumption would still increase! It's just that consumption, or quantity demanded would increase by a less than proportionate amount compared to the change in price. May 11, 2017 at 12:38
• I'm embarrassed that I screwed up the answer. Thank you both for pointing out the errors and I believe I corrected everything. May 11, 2017 at 13:27