Moreover, according to the other prices demand determinant, a change in the price of one good is also likely to affect the purchase of another good. As such, this particular utility analysis of consumer equilibrium can provide insight into both the law of demand and the other prices demand determinant.

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 Sundae Price Change

To answer this question, the original consumer equilibrium must be reevaluated. If Duncan continues to consume 3 sundaes and 4 pretzels after the sundae price reduction, his total expenditures are only $14 ($6 spent on 3 sundaes and $8 spent on 4 pretzels). In effect, Duncan has an extra $6 of income to spend.

With the lower $2 hot fudge sundae price, Duncan could purchase up to 3 more sundaes. However, in that the pretzel price is also $2, Duncan could purchase up to 3 additional pretzels, too. In fact, because both goods now carry a $2 price, Duncan could purchase any combination of extra pretzels and sundaes that sums up to 3.

Pretzels and Sundaes

The key to determining the extra quantity of each good purchased is the same as that for the initial consumer equilibrium--the marginal utility-price ratio. Because the price of hot fudge sundaes changes, the marginal utility-price ratio for each quantity also changes. To reveal the new ratios, click the [New Ratios] button in the exhibit to the right. 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 means the rule of consumer equilibrium is now 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.

• Suppose Duncan opts for a fourth sundae. If so, his total expenditure rises to $16, and the marginal utility-price ratio for sundaes falls to 4 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 (4 utils per dollar) is still greater than his pretzel marginal utility-price ratio (3 utils per dollar).


• A fifth sundae seems to be in order. This purchase raises his total expenditure to $18 and drives the sundae marginal utility-price ratio down to 2 utils per dollar. This ratio, however, is now below the 3 utils per dollar pretzel marginal utility-price ratio.


• What about buying another pretzel? A fifth pretzel does the trick of restoring consumer equilibrium. This purchase raises total expenditure to $20. It also drives the marginal utility-price ratio for pretzels down to 2 utils per dollar, achieving equality with the marginal utility-price ratio for 5 hot fudge sundaes.

Summing Up

• Law of Demand: First, consider how the change in the price of hot fudge sundaes affects the quantity of hot fudge sundaes purchased. The price decreases and the quantity increases. This reflects the basic inverse relation between demand price and quantity demanded that is the law of demand.


• Other Prices Demand Determinant: Second, consider a change in the price of hot fudge sundaes affects the quantity of pretzels purchased. The price of sundaes decreases and the quantity of pretzels increases. This particular example suggests a complementary relation between pretzels and sundaes.