Consumption Options

Pretzels and Sundaes

The left half of the table summarizes the utility numbers for Duncan's pretzel consumption. As Duncan consumes up to 6 pretzels, his total utility rises to a peak of 42 utils before declining for the seventh. 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 before declining for the sixth and seventh 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). Clearly overindulgence is not a good thing for Duncan.

Duncan's challenge is to select the most satisfying, utility maximizing, combination of pretzels and hot fudge sundaes.

No Limits

Pretzels and Sundaes

This result illustrates a simple, and to be quite honest, largely uninteresting consumer equilibrium. Duncan has simply consumed until he can consume no more. He has satiated his want (or need) for pretzels and hot fudge sundaes.

Income and Prices

Consider a couple of alternative ways Duncan could spend his $20 on sundaes and pretzels.

• Nothing But Sundaes: Duncan could spend his entire $20 on sundaes. In this case, he could purchase 5 Hot Momma Fudge Bananarama Ice Cream Sundaes and generate 60 utils of total satisfaction. Unfortunately, no income remains to purchase any of Max Mulroney's tasty Pretzels-on-a-Stick. Duncan's utility total is maxed out at 60 utils. Click the [All Sundaes] button to highlight this option.


• Mainly Pretzels: Alternatively, Duncan could "go nuts" buying pretzels. Of course, once he purchases 6 of Max Mulroney's Pretzels-on-Sticks, reaching his maximum pretzel-based utility of 42 utils, he has no reason to buy the seventh. The seventh pretzel actually reduces his utility. However, these 6 pretzels use up only $12 of Duncan's $20 budget. What might Duncan do with the remaining $8? How about buying 2 sundaes, which generates 36 utils? His total utility for this option is 78 utils--42 utils from 6 pretzels and 36 utils from 2 sundaes. Click the [Mostly Pretzels] button to highlight this option.


• One More Sundae: The second alternative certainly generates more total utility than the first, but can Duncan do even better? Suppose Duncan decides to buy one more sundae, bringing his sundae total to 3. However, to do so, he needs an extra $4. This can only come from cutting back on pretzel purchases. Duncan would have to buy two fewer pretzels (saving $2 each), bringing his new pretzel quantity to 4.

  On the sundae side of utility, Duncan obtains 48 utils of satisfaction from 3 sundaes. On the pretzel side, he has 36 utils from 4 pretzels. His grand utility total of 84 utils exceeds either of the two previous alternatives. Click the [Constrained Max] button to highlight this option.



• Yet Another Sundae?: But can Duncan push his utility even higher? If a third sundae boosts total utility, maybe a fourth one does, too. Once again, though, an extra sundae means Duncan must give up two pretzels. Pursuing this option gives Duncan 78 utils of satisfaction--56 utils from 4 sundaes and 22 utils from 2 pretzels--which is clearly below the 84 utils from 3 sundaes and 4 pretzels. Click the [Too Many Sundaes] button to highlight this option.

As a matter of fact, Duncan's utility is maximized with 3 sundaes and 4 pretzels. He cannot buy any other combination of sundaes and pretzels with his $20 and receive a higher level of total utility.

The Rule of Consumer Equilibrium

• The Sundae Ratio: With a price of $4 each, the marginal utility of the third sundae (12 utils) means that the last dollar Duncan spends on sundaes generates 3 utils of satisfaction.


• The Pretzel Ratio: Moreover with a purchase price of $2, the marginal utility of the fourth pretzel (6 utils) means that the last dollar Duncan spends on pretzels also generates 3 utils of satisfaction.