• One, the law of diminishing marginal utility means that the marginal utility obtained from consuming a good declines as the quantity consumed increases.


• Two, the marginal utility of a good underlies the demand price that buyers are willing and able to pay for a good.

When combined, these two propositions indicate the demand price that buyers are willing and able to pay for a good declines as the quantity demanded (and consumed) increases, which is the law of demand.

Starting with Utility

Edgar Rides the Coaster

But first, consider the marginal utility curve itself.

• The vertical axis measures marginal utility in utils and the horizontal axis measures quantity in rides on the roller coaster.


• The marginal utility curve has a negative slope, illustrating the law of diminishing marginal utility.


• Marginal utility curve intersects the horizontal axis at 6 rides. Marginal utility is positive up to that point, then becomes negative after.

Adjusting the Rule

marginal utility of good 1 price of good 1

=

marginal utility of good 2 price of good 2

However, in the derivation of Edgar's demand curve for roller coaster rides, the key comparison is not between roller coaster rides and ONE other good, but with ALL other alternatives. The big assumption, therefore, is that Edgar achieves consumer equilibrium and satisfies this rule of consumer equilibrium for ALL other goods.

If so, then Edgar has a "standard" or "benchmark" marginal utility-price ratio. For the sake of exposition, suppose that Edgar's benchmark marginal utility-price ratio is 2 utils per dollar. In other words, Edgar purchases all sorts of different goods such that the last dollar spent on each good generates 2 utils of satisfaction.

It this case, it is possible to specify the rule of consumer equilibrium as:

marginal utility of roller coaster rides price of roller coaster rides

=

marginal utility of all other goods price of all other goods

= 2 utils per dollar

If this equation is rearranged just a little, the result is:

marginal utility of roller coaster rides 2 utils per dollar

=

price of roller coaster rides

The beauty of this equation is that the price that Edgar is willing and able to pay for roller coaster rides (his demand price) is now connected to the marginal utility derived from those rides.

Making the Conversion

The Conversion

Not much changes upon clicking the [Demand Curve] button. One change is the measurement units on the vertical axis from utils to dollars. The other change is the elimination of that part of the curve in the negative range of marginal utility and price (negative prices are not relevant). Feel fee to click the [Reset] and [Demand Curve] buttons a couple of times to confirm that not much changes.