APPENDIX 9-A. RELATIVE PRICE ELASTICITY OF DEMAND FOR 

COMMERCIAL CLOTHES WASHERS

TABLE OF CONTENTS

9-A.1 INTRODUCTION .........................................................................................................1

9-A.2 IMPLIED PRICE ELASTICITY...................................................................................1

9-A.2.1 Implied Price Elasticity Estimation Method..................................................................2

9-A.2.2 Price Elasticity Over Time.............................................................................................4

9-A.2.3 Discussion of Relevant Economic Theory.....................................................................4

9-A.3 PRICE IMPACTS ON THE MARKET SHARE OF FRONT AND TOP 

LOADER CLOTHES WASHERS ................................................................................6

LIST OF TABLES

Table 9-A.2.1 Price elasticity of demand for laundry equipment and other appliances 

and durables.......................................................................................................2

Table 9-A.2.2 Route Operator Revenue by Business Activity: Coinmach ($ million).............3

Table 9-A.2.3 Price Elasticity Decrease after CCW Price Change...........................................4

9-A-i
APPENDIX 9-A. RELATIVE PRICE ELASTICITY OF DEMAND FOR CLOTHES 

WASHERS

9-A.1 INTRODUCTION

This appendix describes the methods used by DOE to estimate price elasticity of demand 

and cross-price impacts for commercial clothes washers.

9-A.2 IMPLIED PRICE ELASTICITY

The price elasticity of demand describes the responsiveness of the quantity purchased of 

a product to a change in its price, and can be generically defined as the ceteris paribus percent 

change in shipments given a 1% change in price, or:

eedd = PP0

QQ0

∗

∂∂

∂∂

where P and Q represent price and shipments quantity, respectively.1

Goods for which a 1% change in price leads to a greater than 1% change in quantity 

demanded are considered “elastic,” while goods for which a 1% change in price leads to a less 

than 1% change in quantity demanded are “inelastic.” The more elastic a given product, the more 

a change in cost that translates into a change in price will alter the demand for the product.

DOE believes that CCW are highly price inelastic and applies a default price elasticity of 

demand of zero for this product, meaning that any cost and price increases resulting from 

efficiency standards are unlikely to substantially affect the quantity of CCW demanded. As 

CCW are a somewhat niche product, estimates of CCW price elasticity were not found in the 

literature, and DOE does not have the necessary data to perform an accurate independent 

calculation of CCW price elasticity. Instead, the value of zero is based on DOE’s understanding 

of the CCW market and distribution channels, particularly in relation to the demand for laundry 

services.

In the case of CCW, consumer price elasticity of demand for laundry services, rather than 

laundry equipment is most relevant. However, in the absence of any specific estimates of 

laundry service price elasticity, laundry equipment price elasticity can provide useful insights. 

Table 9-A.2.1 compares the price elasticity of demand for residential laundry equipment and 

other durable goods, demonstrating that demand for clothes dryers and clothes washers tends to 

be somewhat less elastic than for other appliances and durables. Inelastic demand for laundryrelated products suggests that demand for laundry services is likely inelastic as well. As 

9-A-1
demonstrated in Table 9-A.2.1, laundry equipment appears to be somewhat less price elastic than 

other types of appliances and durables.

Table 9-A.2.1 Price elasticity of demand for laundry equipment and other appliances 

and durables

Product Price elasticity of demand Source

Residential Clothes Dryer -0.14 Golder and Tellis 2

Residential Clothes Washer -0.27 Dale and Fujita 3

Dishwasher -0.43 Dale and Fujita 3

Dishwasher -0.42 Golder and Tellis 2

Room Air Conditioner -0.37 Golder and Tellis 2

Refrigerator -0.37 Revelt and Train 4

Refrigerator -0.35 Dale and Fujita 3

Automobiles -1.07 Hymans 5

Automobiles -0.36 Hymans 5

9-A.2.1 Implied Price Elasticity Estimation Method

To validate the use of a price elasticity of zero, DOE estimates an implied CCW price 

elasticity based on known variables describing the market for laundry services. CCW price 

elasticity is approximated as follows:

IIIIIIIIII II eedd,CCCCCC = eedd,LLLLLLLL LLLLLLLLLL ∗ � PPPP PP CCCCCC

PPPP PP LLLLLLLL LLLLLLLLLL�

where, 

eedd,CCCCCC = price elasticity of demand for commercial clothes washers,

eedd,LLLLLLLL LLLLLLLLLL = average price elasticity of demand for laundry service,

PPPP PP CCCCCC = CCW wholesale price (or cost), and

PPPP PP LLLLLLLL LLLLLLLLLL = price (or cost) of providing laundry service.

Based on review of the literature, an exact value of the price elasticity of demand was not 

identified, but a likely range was established: − 1.0 < eedd,LLLLLLLL LLLLLLLLLL ≤ −0.5. Schettkat and 

Yocarini (2006) note a range of -0.53 to -0.47 (averaging -0.5) for the average price elasticity of 

service demand in the U.S.6 Laundry service is expected to be more of a necessity than luxury, 

and thus the price elasticity of demand is modeled as inelastic, with a bounding value of -1.0. 

For example, Kemp (1998) provides a discussion of the relationship between luxury-necessity 

status and price elasticity for a variety of goods and services.7

The provision of laundry services involves other aspects, including equipment and 

services, beyond the simple rental or sale of a clothes washer. As described by Coinmach 

Corporation, a major route operator, in a recent 10-K annual financial report to the SEC, route 

operator core business activities center around “leasing laundry rooms from building owners and 

9-A-2
property management companies, installing and servicing laundry equipment, collecting 

revenues generated from laundry machines and operating retail laundromats;” additionally, route 

operators “rent laundry machines and other household appliances to property owners, managers 

of multi family housing properties, individuals and corporate entities,” and may engage in 

laundry equipment distribution.8

Coinmach reports revenue by individual business activities in their SEC 10-K report: route, 

rental, and distribution.8, 9 “Route” refers primarily to laundry room leasing and management 

activities; “rental” refers to revenue from leasing clothes washers and dryers; “distribution” 

refers to equipment wholesaling activities.

Route activities related to laundry room or laundromat design, installation, and maintenance are 

not likely to be substantially altered by a change in the price of CCW, but rental and distribution 

revenue are more directly influenced by CCW features and costs. A route operator generally 

both rents CCW to a building owner and manages the laundry space.

10

Table 9-A.2.2 Route Operator Revenue by Business Activity: Coinmach ($ million)

Business Activity FY 2007 FY 2006 FY 2005 FY 2004

Route 492.1 481.7 472.5 469.6

Rental 38.4 36.1 34.4 32.6

Distribution 24.8 25.7 31.7 28.9

Rental % of total 6.9% 6.6% 6.4% 6.1%

Rental +Distribution % 

of total 11.4% 11.4% 12.3% 11.6%

Source: Coinmach Corporation (2005; 2007)

From Coinmach’s ratios of the route, rental, and distribution revenue categories in 2004 -

2007, DOE estimates that PP PP PPCCCCCC

PP PP PPLLLLLLLLLLLLLLLLLLLL

= 0.061 to 0.123. 

Combining the above data inputs, 

IIIIIIIIII II eedd,CCCCCC llll = eedd,LL ∗ � PPPP PP CCCCCC

PPPP PP LLLLLLLL LLLLLLLLLL� = −0.5 ∗ 0.061 = −0.031

IIIIIIIIII II eedd,CCCCCC h iih = eedd,LLLLLLLL LLLLLLLLLL ∗ � PPPP PP CCCCCC

PPPP PP LLLLLLLL LLLLLLLLLL� = −1.0 ∗ 0.123 = −0.123

DOE estimates an implied price elasticity of demand for CCW of approximately -0.03 to 

-0.12 based on the laundry equipment distribution channels and market for laundry services. 

DOE notes that values in this range are quite low, and feels that this exercise supports the use of 

a price elasticity of zero.

A further factor to consider is that CCW price is in some cases not readily apparent to the 

building owner. CCW price is also unknown by the end user of the product, whose demand for 

laundry services drives building owner demand for laundry equipment and laundry room or 

laundromat management services. CCW are generally leased at a monthly rate, so the building 

9-A-3
owner is exposed to only a portion of the total CCW cost increase, based on the ratio of their 

lease term to the expected CCW useful life. If the CCW price is not visible, the consumer will 

not have a price signal to react to. As the implied price elasticity estimate assumes consumer 

awareness of the CCW price, it is likely an overestimation.

9-A.2.2 Price Elasticity Over Time

Price elasticity for a given product is not constant over time; numerous studies have 

demonstrated decreases in price elasticity for durable goods as the period of time since a price 

change increases.5, 11, 12 Similarly, decreases in price elasticity have been demonstrated through 

the stages of a product’s life cycle.

13 DOE projects that any non-zero CCW price elasticity will 

decrease over time, following the proportional decreases demonstrated for automobiles (Table 9-

A.2.3).5

Table 9-A.2.3 Price Elasticity Decrease after CCW Price Change

Years Following Price Change 

1 2 3 5 10 20

Price Elasticity of Demand -1.20 -0.93 -0.75 -0.55 -0.42 -0.40

Relative Change in Elasticity to 

1st year 1.00 0.78 0.63 0.46 0.35 0.33

Implied Price Elasticity (low) -0.031 -0.024 -0.015 -0.007 -0.002 -0.001

Implied Price Elasticity (high) -0.123 -0.096 -0.060 -0.028 -0.010 -0.003

Source: Hymans (1971) and DOE calculations

While estimated to be small initially, the CCW implied price elasticity of demand further 

approaches zero in the years following any price change due to standards. DOE believes that 

using a price elasticity of zero, rather than a small non-zero price elasticity, will introduce at 

most a negligible increase in the probability of error in downstream analyses. An alternative 

scenario using the value of -0.12 is also available as a sensitivity analysis.

9-A.2.3 Discussion of Relevant Economic Theory

Demand for commercial clothes washers can be viewed as a form of derived demand; 

what end users want are laundry services, what apartment and laundromat owners want is an 

avenue to provide laundry services, of which the commercial clothes washer as defined in this 

rulemaking is only one input. Other inputs include clothes dryers and other laundry equipment, 

water and energy, building space, change machines, and labor for maintenance and management.

While many discussions of derived demand in the literature come from the realm of labor 

economics and focus on the relationship between demand for labor and demand for a final 

product whose inputs include labor and capital and possibly other inputs, many if the major 

insights can still be applied to the case of demand for an input (CCW) and demand for a service 

whose inputs include CCW and the other inputs described above.

9-A-4
The four key Marshallian rules of derived demand, as restated by Pigou (1932), are as 

follows:14

1) "The demand for anything is likely to be more elastic, the more readily substitutes for 

that thing can be obtained." (p. 682) 

2) "The demand for anything is likely to be less elastic, the less important is the part played 

by the cost of that thing in the total cost of some other thing, in the production of 

which it is employed." (p. 683) 

3) "The demand for anything is likely to be more elastic, the more elastic is the supply of 

co-operant agents of production." (p. 684) 

4) "The demand for anything is likely to be more elastic, the more elastic is the demand for 

any further thing which it contributes to produce." (p. 685) 

In the preceding treatment of CCW price elasticity, DOE draws largely on rules 2 and 4, 

for which some relevant data is available. Below, the rules are discussed in the context of CCW.

Considering rule 1, from the end-user viewpoint some substitutes for laundry services 

provided by covered CCW in common area laundry facilities or laundromats may exist. It is 

possible that some end-users could instead purchase and use a residential clothes washer, 

assuming that their housing unit has appropriate laundry hook-ups. An additional possibility is 

that end-users may begin to favor types of CCW not covered by this rule if there is a sizeable 

increase in the cost of using a residential-style CCW but not of a larger hard-mount CCW. These 

are fairly similar though imperfect substitutes; they can potentially accomplish the purpose of 

providing laundry services, but each involves additional factors that differ from the covered 

CCW. From the service provider’s perspective, residential-style soft-mount CCW and other 

CCW types may or may not be interchangeable, depending on the space they have available. 

The effect of end-user’s preferences for certain washer types will be limited by physical building 

constraints. While there are some substitutes available for covered CCW, DOE does not believe 

that they will be so readily interchanged as to strongly influence the overall price elasticity of 

demand for CCW.

Hamermesh (1993) rephrases rule 2: “the demand for an input that accounts for a small 

share of costs will be less elastic, other things equal, because the scale effect will be very 

small.”15 As the cost of CCW equipment is only a small portion of the total cost of providing 

laundry services (as demonstrated by the relative shares of route operator revenue from 

equipment rental/sale and other services), rule 2 suggests that this fact supports an inelastic 

demand for CCW. This is incorporated into the estimation equation in the factor PP PP PPCCCCCC

PP PP PPLLLLLLLLLLLLLLLLLLLL

.

Restating rule 3 in terms of the present example, demand elasticity for CCW is expected 

to be more inelastic if the process of providing laundry services makes use of other inputs that 

are highly inelastic in supply. Other inputs, in this case, include other laundry equipment, labor, 

capital, and building space. DOE does not have sufficient information on the elasticity of supply 

for the other inputs of production to directly incorporate this factor into the estimation equation; 

9-A-5
DOE believes that the influence of these other factor is unlikely to overturn the conclusion that 

CCW price elasticity of demand is quite inelastic.

Regarding rule 4, the demand for CCW is likely to be less elastic, the less elastic the 

demand for laundry services. DOE believes laundry services to be more of a necessity than 

luxury, leading to the factor − 1.0 < eedd,LLLLLLLL LLLLLLLLLL ≤ −0.5 incorporated into the estimation equation.

9-A.3 PRICE IMPACTS ON THE MARKET SHARE OF FRONT AND TOP 

LOADER CLOTHES WASHERS

While DOE expects commercial clothes washers in aggregate to be highly price-inelastic, 

substitution between types of washers (i.e. front- and top-loading) may occur if the change in 

price due to standards is not uniform across types. The cross-price impact is estimated to model 

likely switching across product classes.

Due to insufficient data, DOE was not able to estimate cross-price impacts on the market 

share of top-loading and front-loading commercial clothes washers, and instead relies on its recent 

analysis performed for residential clothes washers.16 Analysis methods and results are summarized 

below.

In order to estimate the impact of price changes on market share, DOE applied a logistic 

regression method to regress market share on price variables and other attributes. The basic form of a 

logistic regression is: 

= � 1

1 + ee−�ββ0+ββ1xx1,ii+⋯+ββkkxxkk,ii�

�

With some simple operations, the model can be transformed to an equivalent log-linear form:

ll �

1 − � ββ0 + ββ1xx1, + ⋯ + ββkkxxkk,

In this case, is the market share of either top- or front-loading clothes washers, and 

ppii

11−ppii

is the ratio of clothes washer market shares, i.e., the relative probability of the market share 

of top and front-loading clothes washers. The explanatory variables include price-related 

variables, washer size and other washer attributes. The logistic regression model equation 

estimated in DOE’s residential clothes washer analysis is shown below.

ll � MMMM MM MMMMh FF FF FF

1 − MMMM MM MMMMh FF FF FF

� = −2.985386 + 0.0035452 ∗ PPPP PP TT TT + 4.24347 ∗ � SS FF FF FF

SS TT TT

�

Where:

9-A-6
MM h FF FF FF

1−MM h FF FF FF

 = relative probability of the market share of front- and top-loading clothes 

washers,

PPPP PP TT TT = weighted monthly average price of top-loaders,

PPPP PP FF FF FF = weighted monthly average price of front-loaders, and SS FF FF FF

SS TT TT

= ratio between the monthly weighted average of front-loaders tub volume 

and the monthly weighted average of top-loaders tub volume.

The equation indicates that front loader market share is positively correlated with top 

loader price and size and negatively correlated with front loader price (all variables in this 

regression were statistically significant; the R2 in the regression was 0.88).

The price coefficients suggest that top- and front-loading washers are substitutes for each 

other. The positive coefficient associated with the size variable indicates that capacity is a 

desirable clothes washer feature for most consumers.

These regression results were used to derive the cross price impact of a change in the 

front loading washer price on the top loading market share (and vice versa). For example, these 

results suggest that a 10% increase in the price of front loader washers would lead to a 10.7 %

decrease in top-loader market share, holding other variables constant and measured as changes 

from the reference case using average values for each variable. In this case, the front-loading 

cross-price impact (percent change in top-loading market share over percent change in frontloading price) is 1.07. Note that price elasticity varies according to the reference price and 

market share, typically measured as changes from mean values for these variables in the data set. 

In DOE’s dataset, the reference top-loading washer price is $403.78, the reference front-loading 

washer price is $823.83, the corresponding reference top-loading washer market share is 71% 

and the corresponding reference front washer market share is 29%.

Similarly, these results indicate that a 20% price increase for top-loading washers would yield a 

21.49 % increase in front-loading market share, measured as changes from the variable means. 

Thus, in this example the top-loader cross-price impact is also 1.07. See the residential clothes 

washers 2012 Direct Final Rule Technical Support Document for additional details.16

9-A-7
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m>

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htm>

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in the Presence of Reference Price Effects. Journal of the Academy of Marketing Science, 

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12. Gowrisankaran, G. and M. Rysman, Dynamics of Consumer Demand for New Durable 

Goods. 2009, National Bureau of Economic Research Working Paper: Cambridge, MA. 

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13. Lilien, G. L. and E. Yoon, An Exploratory Analysis of the Dynamic Behavior of Price 

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16. U.S. Department of Energy, Technical Support Document: Energy Efficiency Program 

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D.C. 

9-A-9