﻿ Estimating Demand Curves and Elasticities

# Estimating Demand Curves and Elasticities

Before outlining simulation strategies for pricing research, we should give a few notes of caution.  The ACA system is often not a very good pricing research tool; CVA and particularly the CBC and ACBC systems are considered stronger approaches for most markets.

We will build upon the previous example during this section.  We previously computed shares of preference for three products defined using the following attribute level codes:

Product Specifications:

Product Name Brand Style Price

"BrandA"        1      1      1

"BrandB"        2      2      3

"BrandC"        3      3      2

You may recall that price levels 1, 2 and 3 correspond with the following prices \$100, \$150, and \$200.  The shares of preference for the products as defined above were:

Shares of Preference for Products:

BrandA            42.5

BrandB            21.3

BrandC            36.2

Let's assume we wanted to estimate a demand curve for your company's offering: BrandC, in the context of the current competition and prices.  We do this through "sensitivity analysis."  The choice simulator offers an automatic way to conduct sensitivity analysis, but so you understand the process, we'll describe it in separate steps.

Recall that we measured three distinct levels of price \$100, \$150 and \$200.  Note that we've already computed the share of preference for BrandC when it is offered at \$150 (36.2).

To estimate the demand curve for BrandC, we'll need to conduct two additional simulations: a simulation with BrandC at the lowest price (\$100) and a simulation with BrandC at the highest price (\$200).  For each of these simulations, we'll hold the BrandA and BrandB product specifications constant.

To estimate BrandC's share at the lowest price (\$100), we use the following product specifications:

Product Specifications:

Product Name Brand Style Price

"BrandA"        1      1      1

"BrandB"        2      2      3

"BrandC"        3      3      1

We run the simulation and the following shares are reported:

Shares of Preference for Products:

BrandA            33.9

BrandB            15.6

BrandC            50.5

We record BrandC's share (50.5), and proceed to the next step. To estimate BrandC's share at the highest price (\$200), we use the following product specifications:

Product Specifications:

Product Name Brand Style Price

"BrandA"        1      1      1

"BrandB"        2      2      3

"BrandC"        3      3      3

We run the simulation and the following shares are reported:

Shares of Preference for Products

BrandA         49.2

BrandB         26.9

BrandC         23.9

From these three separate simulation runs, we now have all the information we need to plot a demand curve for BrandC, relative to the existing competitors and prices.  Assuming that BrandA and BrandB are held constant at current market prices, the relative shares of preference for BrandC at each of the price points within the measured price range are:

Share of

Price   Preference

\$100      50.5

\$150      36.2

\$200      23.9

We have demonstrated how to estimate a demand curve for BrandC, relative to the existing competitors at current market prices.  If the goal is to estimate demand curves for all brands in the study, the usual procedure is to record the share for a brand at each price level while holding all other brands at the average (middle) price.  It is often interesting to plot these demand curves and look at the patterns of price sensitivity between brands and the different slope of the curves from one segment of the curve to the next.  It is also common to want to characterize the degree of price sensitivity using a single value, referred to as an elasticity.  The Price Elasticity of Demand (E) is defined as:

E =        %rQ

 %rP

where,

"%r" means "percent change in,"

Q is defined as quantity demanded, and

P refers to the price.

If the brand or product follows the law of supply and demand (most products do), price increases lead to decreases in quantity demanded, and the elasticity is negative.  The larger the absolute value of the elasticity, the more price sensitive the market is with respect to that brand or product.

Using the "midpoints" formula, we can compute the average price elasticity of demand across the demand curve for BrandC:

E = q2 – q1         ÷       p2 – p1

(q1+q2)/2                (p1+p2)/2

23.9 – 50.5       ÷       200 – 100

(50.5+23.9)/2             (100+200)/2

-0.715           ÷        0.667

=  -1.073

Another way to compute the average price elasticity of demand (which is especially useful if more than two price points along the curve have been estimated) is the "log-log" regression.  One takes the natural log of prices and shares and regresses the log of share on the log of price (you can do this within a spreadsheet).  The resulting beta is the average price elasticity of demand.

As with all conjoint simulation results, the resulting elasticities from choice simulators are interpreted bearing in mind some assumptions.   In particular, the degree of noise within the conjoint data is particularly relevant.  For example, if the respondents to the conjoint survey answered in a more haphazard way compared to buyers in the real world, the price elasticities estimated from conjoint simulations may be uniformly understated (too insensitive).  Also, you should recognize that changing the Exponent will shift the elasticities.  Even if this is the case, the relative price sensitivities for brands are still useful.