A Review of Consumer Equilibrium

Pretzels and Sundaes

• Two Goods: The table at the right presents utility information for Duncan Thurly, a snack-hunger consumer who is purchasing 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. The utility story for Duncan's hot fudge sundae consumption is in the right half of the table.



• Income and Prices: Duncan's initial choice of pretzels and hot fudge sundaes is based on a snack purchasing income of $20, a pretzel price of $2, and a hot fudge sundae price of $4.


• The Choice: Under these circumstances, Duncan selects 4 pretzels and 3 hot fudge sundaes, spending $8 on pretzels and $12 on hot fudge sundaes.


• Consumer Equilibrium: This combination satisfies the rule of consumer equilibrium and equates the marginal utility-price ratio for each good. The marginal utility of the last pretzel is 6 utils, giving a marginal utility-price ratio of 3 utils per dollar. The marginal utility of the last hot fudge sundae is 12 utils, also resulting in a marginal utility-price ratio of 3 utils per dollar. Consumer equilibrium is achieved.


• Utility Maximization: With consumer equilibrium, utility is maximized at a total of 84 utils. The purchase of 4 pretzels generates 36 utils of satisfaction and the consumption of 3 hot fudge sundaes adds another 48 utils. No other combination of pretzels and hot fudge sundaes purchased with $20 of income and the existing prices generates a greater level of utility.

A Change Sundae Preferences

Pretzels and Sundaes

This change in preferences is reflected by a change in the total utility and marginal utility derived from sundae consumption. Click the [New Preferences] button to illustrated this change. The new numbers indicate that Duncan likes hot fudge sundaes substantially more than before the change.

For example, prior to the change, Duncan receives a total of 48 utils for consuming 3 hot fudge sundaes. After the change he receives a total of 84 utils for the same quantity. Moreover, the marginal utility of the third sundae is 12 utils before the preference change and 24 utils after the change. This is just the sort of change that is bound to disrupt consumer equilibrium and throw the rule of consumer equilibrium out of balance.

The key to identifying the imbalance and determining the new consumer equilibrium is the marginal utility-price ratio. Because the hot fudge sundae marginal utilities change, the marginal utility-price ratios also change. The new ratios, given the existing $4 price, are also presented in the table. Note that for each hot fudge sundae, Duncan now receives a greater level of satisfaction per dollar spent.

This new set of marginal utility-price ratios reveals that the original purchase of 3 sundaes generates 6 utils per dollar, compared to the initial ratio of 3 utils per dollar. Moreover, this new ratio confirms that the rule of consumer equilibrium is out of balance. The fourth pretzel generates 3 utils per dollar, but the third sundae generates 6 utils per dollar.

Because Duncan receives a greater amount of satisfaction per dollar spent on sundaes, it seems reasonable for him to purchase more sundaes, fewer pretzels, or a combination of the two. Of course, given that his income remains at $20, if he chooses to buy more sundaes, he must necessarily purchase fewer pretzels.

• Suppose Duncan opts for a fourth sundae. If so, his total expenditure rises to $24, and the marginal utility-price ratio for sundaes falls to 5 utils per dollar. While this moves him closer to consumer equilibrium, the rule of consumer equilibrium remains out of balance. His sundae marginal utility-price ratio (5 utils per dollar) is still greater than his pretzel marginal utility-price ratio (3 utils per dollar). Even worse, the $24 expenditure exceeds his $20 budget.


• Duncan can reduce his total expenditure by the $4 needed to achieve his $20 budget if he consumes 2 fewer pretzels. In so doing, the marginal utility of pretzels increases, working the law of diminishing marginal utility in reverse, which then causes the pretzel marginal utility-price ratio to rise. If Duncan decides to consume 2 pretzels rather than 4, his total expenditure declines to $20 and the pretzel marginal utility-price ratio rises to 5 utils per dollar.