Thursday  September 23, 2021
 AmosWEB means Economics with a Touch of Whimsy!
 COMMON-PROPERTY GOOD: A good that's difficult to keep nonpayers from consuming, but use of the good by one person prevents use by others. Examples include oceans, the atmosphere, many lakes and streams, and large tracts of wilderness area or public parks. The term "common property" aptly describes the situation here, it's commonly owned and thus everyone has access to it, but it can be easily used up or destroyed. Many of our pollution problems occur because common property becomes a convenient place to dump waste materials. For efficiency, government needs to take charge of common-property goods, private exchange through markets can't do the job.

RULE OF CONSUMER EQUILIBRIUM:

A condition of consumer equilibrium and utility maximization stating that the marginal utility-price ratios for all goods are equal. This rule is a handy way of checking for consumer equilibrium and utility maximization. If the rule is not satisfied, then consumer equilibrium and utility maximization are not achieved.
The rule of consumer equilibrium is satisfied when a consumer selects a combination of goods that maximizes utility. With utility maximization, a consumer cannot increase utility by consuming more of one good and less of another. This occurs because the marginal utility-price ratio for each good is the same. In other words, consumers generate the same amount of utility from the last dollar spent on each good.

### A Handy Formula

The following equation summarizes the rule of consumer equilibrium for two goods (ingenuously labeled good 1 and good 2). While this equation is only for two goods, in principle, it applies to any number of goods.

 marginal utility of good 1price of good 1 = marginal utility of good 2price of good 2

### Working a Few Numbers

Pretzels and Sundaes
The rule of consumer equilibrium can be illustrated using this table summarizing Duncan Thurly's snack consumption of two goods, Max Mulroney's Pretzel-on-a-Stick and Hot Momma Fudge Bananarama Ice Cream Sundae.

The left half of the table summarizes the utility numbers for Duncan's pretzel consumption. As Duncan consumes pretzels, up to 6, his total utility rises to a peak of 36 utils before declining. His marginal utility for pretzel consumption begins at 12 utils for the first pretzel, then declines (according to the law of diminishing marginal utility) until reaching -2 utils for the seventh one.

The utility story for Duncan's hot fudge sundae consumption in the right half of the table follows a similar pattern, albeit with different numbers. Duncan's total utility reaches a maximum of 60 utils for consuming 5 hot fudge sundaes. His marginal utility begins at 20 utils for the first hot fudge sundae then declines to -8 utils for the seventh (also following the law of diminishing marginal utility).

Now suppose that the price of Hot Momma Fudge Bananarama Ice Cream Sundaes is \$4, the price of a Max Mulroney's Pretzel-on-a-Stick is \$2, and Duncan has \$20 of income. Under these circumstances Duncan maximizes utility by consuming 4 pretzels and 3 hot fudge sundaes. Click the [Utility Max] to highlight this combination.

Given that the marginal utility of Duncan's Third hot fudge sundae is 12 utils and the price is \$4, the marginal utility-price ratio for hot fudge sundaes is three to one. Duncan gets 3 utils of satisfaction for the last \$1 spent on sundaes.

 marginal utility of hot fudge sundaesprice of hot fudge sundaes = 12 utils\$4 = 3 utils per dollar
Given that the marginal utility of Duncan's Fourth pretzel is 6 utils and the price is \$2, the marginal utility-price ratio for Max Mulroney's Pretzel-on-a-Stick is also three to one. Duncan gets 3 utils of satisfaction for the last \$1 spent on pretzels.
 marginal utility of pretzelsprice of pretzels = 6 utils\$2 = 3 utils per dollar
While this combination of pretzels and hot fudge sundaes might be an unhealthy diet, at least Duncan has satisfied the rule of consumer equilibrium. The last dollar spent on each good generates the same utility. And because Duncan cannot increase his total utility by consuming more of one good and less of another, he has also achieved utility maximization.

### Breaking the Rule

If the rule of consumer equilibrium is not satisfied, then utility is not maximized and can be increased by changing the combination of goods consumed. Suppose, for example, that Duncan decides to forego the third hot fudge sundae, and the 12 utils of satisfaction that it generates, to consume more pretzels. The \$4 hot fudge sundae price can be used to purchase two additional pretzels.

In this case, Duncan consumes 2 hot fudge sundaes and 6 pretzels. Considering the law of diminishing marginal utility, the marginal utility of pretzels decreases from 6 utils to 2 utils. Working in the reverse direction, the marginal utility of hot fudge sundaes increases from 12 utils to 16 utils.

The new marginal utility-price ratio for hot fudge sundaes increases to 4 utils per dollar, based on the \$4 price and the 16 utils of satisfaction.

 marginal utility of hot fudge sundaesprice of hot fudge sundaes = 16 utils\$4 = 4 utils per dollar
The new marginal utility-price ratio for pretzels decreases to 1 util per dollar, based on the \$2 price and the 2 utils of satisfaction.
 marginal utility of hot pretzelsprice of pretzels = 2 utils\$2 = 1 util per dollar
This situation is not good. Duncan is better off with 3 sundaes and 4 pretzels than with 2 sundaes and 6 pretzels. He is not satisfying the rule of consuming equilibrium. A quick check of the utility numbers in the table above also indicates that Duncan has less utility. The combination of 3 sundaes (with 48 utils) and 4 pretzels (with 36 utils) generates a total utility of 84 utils. The combination of 2 sundaes (with 36 utils) and 6 pretzels (with 42 utils) generates a total utility of 78 utils.

If Duncan does not satisfy the rule of consumer equilibrium then his utility is not maximized.

Recommended Citation:

RULE OF CONSUMER EQUILIBRIUM, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2021. [Accessed: September 23, 2021].

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