# Calculating price elasticity by asking a “this” or “that” question

Let's say 2 goods exist: A for 10 and B for 20 (B is more premium in this example)

If I decrease the price of both goods by 10% and ask:

"Do you prefer A for 9 or B for 18 "

What sort of insights (elasticities, etc.) would I be able to get from this? I figure the usual arc elasticity is not possible for this, since the units are discrete.

Is it also possible to get other insights if I lower the price of the premium product more than the cheap product? i.e.:

"Do you prefer A for 9 or B for 17?"

Or even lower the price of the cheap product more than the premium, i.e,

"Do you prefer A for 8 or B for 18?"

I'm thinking about any insights that I can get from asking these sorts of questions, but the traditional equations of elasticity don't seem to apply.

The elasticity of demand measures how changes in prices affect changes in quantities demanded So if you have the total quantity demanded at the original prices and reduced them by, say, $$10\%$$, then observe the total quantity demanded of both goods, you can calculate elasticity by simply using the arc formula, or the midpoint formula, etc. In fact, by just varying one good at a time, or reducing one good more than the other, you could also estimate cross-price elasticities.

In your example, however, it sounds like you have only information on a single consumer that buys either one good or the other. So you only know if they were buying at the original prices and which good and if they start buying after prices decrease, or if they decide to change the good they buy.

This exercise cannot really measure any elasticity because there is no sensitivity to measure. Best case scenario, if the person was not buying a good and after the decrease in price starts buying it, it can give you a lower bound on their valuation for the good.

In contrast, if the question was changed to how many units of each good would the consumer buy? then you could estimate demand elasticity and cross-price elasticities with careful exercises of lowering each price at a time.

Simple case is following: You decrese price by same % for usual and premium goods, than measure the demand. If both change in same ratios their elasticity is same, and so on.

1. You can meauser the elasticity lag for both cases, when users start reacting to price change for both groups.

2. You can measure behavior of users moving between groups (premium, usual) when price changes.

• Assuming the budget isn't exhausted (I assume the budget must be at least 20 for this problem to really make sense), then there has to be at least a third good. In addition, when goods are discrete or sold discretely, there is no guarantee that $MU_i / p_i$ are equated over all $i$ goods. Additionally, since you're (potentially) switching between A and B, you can't measure a classic elasticity, because that's a percent change in demand for X WRT a percent change in price of x. In this setup, that's always going to be $\pm \infty$ or 0 -- right? – BKay Oct 2 '20 at 15:17