Econ 101: Individual Demand Curves and Willingness to Pay

Holly Hosford-Dunn
April 17, 2012

Last time in this series, we left off with a consumer — who we’ll now name Jack — facing a choice of purchasing hearing aids or monthly golf club membership. We gave Jack a $5000 budget and made it simple by making it a $1000 choice for golf or a hearing aid.  To recap, Jack’s utility, when faced with the choices, is shown in Table 1, demonstrating that he gets more utility from 1 month of golf (5 utils) than he does from one hearing aid (4 utils) and  he gets less utility as he consumes more of either good.  When faced with his $5000 budget (Table 2), he maximizes utility by purchasing 1 hearing aid and 4 months of golf.

Today we’ll complicate things by changing the price of hearing aids to figure out how Jack’s utility table and budget change his demand for hearing aids as a function of Price.  We always refer back to Jack’s utility table (Table 1), but now we consider how Jack’s budget/utility choices change when hearing aids cost $3000 each (Table 3) and $500 each (Table 4).  Jack’s maximum utility is shown is highlighted in green for the different price choices.

We can now combine the information from Tables 2,3 & 4 to construct his individual demand “curve” (Figure 1), which is not so much a curve as a set of discrete choices. He’ll buy two hearing aids if they cost $500/each, one if the price goes up to $1000/each, and he’ll forego hearing aid purchase and use his money for golf if the price goes up to $3000 each.

Figure 1. Jack's Demand for Hearing Aids

Like any Demand Curve, Jack’s preferences show that he will purchase less as Price goes up.  From the Supplier’s point of view — in this case the Dispenser — “Quantity Sold” increases as selling price goes down.  Once again, readers are saying “Duh!”  We knew that without all these tables, figures, and useless utils, right?

Yes, but one step further and you may agree that Utils have Utility to Us.  Let’s assume that Jill moves into town and she has oodles of money. Her utility for golf and hearing aids isn’t the same as Jack’s, of course, but we won’t irritate you further by showing all that. We’ll just overlay her Individual Hearing Aid Demand “Curve” over Jack’s in Figure 2.  Clearly, Jill is willing to spend more on hearing aids than Jack: she’ll buy one if they are $3000/ea and she’ll buy two if they are $500/ea.  In fact, she would think she was getting a real bargain at $500/ea because she would willingly buy two even if the price was $2000/ea.  Jill has experienced what we call “consumer surplus” of $1500/hearing aid if she manages to buy them at $500/ea{{1}}[[1]]We’ll explore consumer surplus in a later post in this series.[[1]]But for now, let’s think about this from the Dispenser’s point of view: what Quantity can the Dispenser expect to sell depending on the selling Price?  Figure 2 tells us that for our “market” of two people, zero hearing aids will be sold at $5000/ea, one hearing aid will be sold at $3000/ea (to Jill), two will be sold at $2000/ea (to Jill), and three will be sold at $1000/ea (one to Jack, two to Jill).  Finally, four will be sold at $500 each (Jack and Jill both buy two).  By combining their consumption choices, we end up with the beginnings of a true Demand Curve, as shown in Figure 3.

When Economists go about constructing Demand Curves, they use logic of this type, but with the big assumption that Jack and every other consumer is not just deciding between hearing aids and golf. For instance, just consider how Jack’s utility table might change if  the monthly golf club dues choice was switched to the average cost of a family’s annual health care deductibles — $3700/year at this point!  Instead, Jack and other consumers make their hearing aid purchase decisions by comparing their utility for hearing aids against all other possible consumption choices that lie within their budgets.  “All other consumption choices” is what Economists mean when they talk about “baskets of goods.” And, when you think about it, that is exactly what every one of us does when we weigh the choice of paying for anything versus using that money for something else.  That is what is meant by “willingness to pay.”

If we jump from a comparison of hearing aids vs golf membership to the more realistic comparison of hearing aids versus all other consumption choices, we can say that a person’s additional willingness to pay decreases with each additional unit consumed.    Economists call that downward willingness to pay a decreasing marginal benefit.  Checking out the corresponding demand function (e.g., Fig 3), you can see that marginal benefit and Price go together — if we know one, we can figure out the other.  If you have access to JAAA, be sure to see the 2001 study by Chisolm and Abrams in which willingness to pay for hearing aid features was correlated with hearing aid benefit reported by US Veterans.{{2}}[[2]]Chisolm TH & Abrams HB.  Measuring Hearing Aid Benefit Using a Willingness to Pay Approach.  JAAA 12 (2001), 383-389.[[2]]

In Summary:  given consumers’ utility maximizations, we can derive their individual Demand Curves and from there we can generalize and figure out their willingness to pay (decreasing marginal benefit) for hearing aids versus all other goods.  And once we know the marginal benefit for additional consumption of hearing aids for many people, we can add up all their individual demand curves and arrive at a demand curve for the entire market. When we’ve got that, we know the maximum Quantity we can dispense at a given Price.  Ta Da!

In the Real World:  Coming up with Demand Curves for a Good requires a huge amount of data on consumer behavior so that Economists can model a variety of choices and control for tons of variable choices as well as other effects (e.g., economic down turn, government policy).  Suffice it to say that we DO NOT have well constructed Demand Curves for hearing aids available in our literature, although some good efforts have been made to initiate their construction.  This is not to say that well-modeled demand curves do not exist.  Vast amounts of consumer data exist, crunched into very expensive, proprietary reports that are purchased by interested parties.  Economic data modeling is yet another technological advantage for which manufacturers compete ferociously.

Future posts in this series will consider factors that affect and change Demand Curves.  Even if we do not know exactly WHAT our demand curves look like, we can and should think hard about factors such as Income and Substitution Effects and what those do to consumers’ purchasing power and consumption choices.  In the meantime, those wishing for a bit more in the way of explanation and equations can increase their Utility by visiting ceteris paribus.{{3}}[[3]]Let me know if you are one of these people. I’m feeling a bit lonely.[[3]]

photo courtesy of The Telegraph

  1. I really liked this article and found it to be very interesting. I think this is one of those concepts that many of us are aware of on some level, but may not think about in such concrete terms. Thanks for having such a nice explanation as well. Lots of numbers in graphic form make my eyes cross!

    1. Holly Hosford-Dunn Author

      I know what you mean about all the numbers and graphs. I worked for a loooong time trying to get it down to as few as possible, but it still turns out to be enough to cross any normal pair of eyes. A lot of the looking and “getting” has to do with familiarity — I find it far easier now that I’ve taken umpteen Econ courses, where all you see if numbers and graphs. I like to think that an economist wandering into an audiometry class might have the same cognitive dissonance at first and leave with his/her eyes crosses in the beginning!

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