APPENDIX 9

- A

. RELATIVE PRICE ELASTICITY OF DEMAND FOR
COMMERCIAL CLOTH E S WASHERS

TABLE OF CONTENTS

9

- A.1 INTRODUCTION

................................ ................................ ................................ ......... 1 9

- A.2 IMPLIED PRICE ELASTI CITY

................................ ................................ ................... 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 R elevant Economic Theory

................................ ................................ ..... 4 9

- A.3 PRICE IMPACTS ON THE MARKET SHARE OF FRON T AND TOP LOADER CLOTHES WASHE RS

................................ ................................ ................ 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

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- iAPPENDIX 9

- A. RELATIVE PRICE ELAST ICITY OF DEMAND FOR CLOTH E S
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 ELASTI CITY

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:

ee dd = PP 0 QQ 0 ∗ ∂∂ ∂∂

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 cha nge 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 calcula tion 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 fo r 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 ela sticity 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 laundry

related pr oducts suggests that demand for laundry services is likely inelastic as well. As

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- 1demonstrated 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 laundr y 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 ee dd
, CCCCCC = ee dd
, LLLLLLLL LLLLLLLLLL ∗ � PPPP PP CCCCCC PPPP PP LLLLLLLL LLLLLLLLLL �

where,

ee dd
, CCCCCC = price elasticity of demand for comm ercial clothes washers,

ee dd
, 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 o n review of the literature, an exact value of the price elasticity of demand was not identified, but a likely range was established:

− 1

. 0 < ee dd
, LLLLLLLL LLLLLLLLLL ≤

− 0

. 5 . Schettkat and Yocarini (2006) note a range of

- 0.53 to

- 0.47 (averaging

- 0.5) for th e 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 elastici ty 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
oper ator core business activities center around “leasing laundry rooms from building owners and

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- 2property management companies, installing and servicing laundry equipment, collecting revenues generated from laundry machines and operating retail laundromats;” ad ditionally, 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 maintenanc e 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 owne r 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 PP CCCCCC PP PP PP LLLLLLLLLLLLLLLLLLLL = 0.061 to 0.123.

Combining the above data inputs,
IIIIIIIIII II ee dd
, CCCCCC llll = ee dd
, LL ∗ � PPPP PP CCCCCC PPPP PP LLLLLLLL LLLLLLLLLL �

= − 0

. 5 ∗ 0

. 061 = − 0

. 031

IIIIIIIIII II ee dd
, CCCCCC h ii h = ee dd
, 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 equipme nt and laundry room or laundromat management services. CCW are generally leased at a monthly rate, so the building

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- 3owner 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 assume s 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 d erived 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 machin es, 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 lab or 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.

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- 4The four key Marshallian rules of d erived 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 to tal 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, t he 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 co uld 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 incre ase 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 tha t 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 w asher 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 CC W.

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 PP CCCCCC PP PP PP LLLLLLLLLLLLLLLLLLLL .

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;

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- 5DOE believes that the i nfluence 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 believ es laundry services to be more of a necessity than luxury, leading to the factor

− 1

. 0 < ee dd
, LLLLLLLL LLLLLLLLLL ≤

− 0

. 5 incorporated into the estimation equation.

9

- A.3 PRICE IMPACTS ON THE MARKET SHARE OF FRON T AND TOP LOADER CLOTHES WASHE RS
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 performe d for residential clothes washers. 16 Analysis methods and results are summarized below.

In order t o 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 − � ββ 0 + ββ 1 xx 1
, ii + ⋯ + ββ kk xx kk

, ii � �

With so me simple operations, the model can be transformed to an equivalent log

- linear form:

ll � 1

− � ββ 0 + ββ 1 xx 1
, + ⋯ + ββ kk xx kk
,

In this case, is the market share of either top

- or front

- load ing clothes washers, and
pp ii 11

− pp ii is the ratio of clothe s washer market shares, i.e., the relative probability of the market share of top and front

- load ing clothes washers. T he explanatory variables include price

- related variables , washer size and other washer attributes. The logistic regress ion model equation estimated in DOE’s residential clothes washer analysis is shown below.

ll � MMMM MM MMMM h FF FF FF 1

− MMMM MM MMMM h FF FF FF �

= − 2

. 985386 + 0

. 0035452 ∗ PPPP PP TT TT + 4

. 24347 ∗ � SS FF FF FF

SS TT TT �

Where:

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- 6MM 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 o f 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 R 2 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 c hange 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 front

loading price) is 1.07

. Note that p rice elasticity varies according to the ref erence 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 fron t

- 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%.

S imilarly, these results indicate that a 20% price increase for top

- loading washers wo uld 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

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- 7REFERENCES

1. Varian, H. R., Intermediate Mic roeconomics: A Modern Approach . 1999. Vol. 5th Edition. W.W. Norton & Company: New York, London.

2. Golder, P. and G. Tellis, Beyond Diffusion: An Affordability Model of the Growth of New Consumer Durables

. Journal of Forecasting , 1998. 17: pp. 259

- 280

3. Dale, L. and K. S. Fujita, An Analysis of the Price Elasticity of Demand for Household Appliances , 2008. Lawrence Berkeley National Laboratory.

4. Revelt, D. and K. Train, Mixed Logit with Repeated Choices: Household's Choice of Appliance Efficiency Level

. Review of Economics and Statistics , 1998. 80(4): pp. 647

- 657 < http://www.mitpressjournals.org/doi/pdfplus/10.1162/003465398557735 >

5. Hymans, S., Consumer Durable S pending: Explanation and Prediction

. Brookings Papers on Economic Activity , 1971. 1971(1): pp. 234

- 239

6. Schettkat, R. and L. Yocarini, The shift to services employment: A review of the literature

. Structural Change and Economic Dynamics , 2006. 17: pp. 127

- 147

7. Kemp, S., Perceiving luxury and necessity

. Journal of Economic Psychology , 1998. 19: pp. 591

- 606

8. Coinmach Corporation, 10

- K Annual Report for Fiscal Year 2005, 2005. SEC EDGAR. (Last accessed November 19, 2012.)

< http://www.sec.gov/Archives/edgar/data/91693/000095012305007218/y09552e10vk.ht

m >

9. Coinmach Corporation, 10

- K Annual Report for Fiscal Year 2007, 2007. SEC EDGA R. (Last accessed November 20, 2012.)

< http://www.sec.gov/Archives/edgar/data/1282858/000095012307008319/y35770e10vk. htm >

10. Mac

- Gray Corporation, 10

- K An nual Report for Fiscal Year 2011, 2011. SEC EDGAR. (Last accessed November 20, 2012.)

< http://www.sec.gov/Archives / edgar/data/103 8280 / 000104746913002858 / a2213463z10

- k.htm >

11. Fibrich, G., A. Gavious, and O. Lowngart, The Dynamics of Price Elasticity of Demand in the Presence of Refe rence Price Effects

. Journal of the Academy of Marketing Science

, 2005. 33(1): pp. 66

- 78

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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- 813

. Lilien, G. L. and E. Yoon, An Exploratory Analysis of the Dynamic Behavior of Price Elasticity over the Product Life Cycle: An Empirical Analysis of Industrial Chemical Products

. Issues in Pricing , 1988: pp. 261

- 408

14. Pigou, A. C., The Economics of W elfare . 4 ed. 1932. MacMillian: London. 682

- 687.

15. Hamermesh, D., Labor Demand . 1993. Princeton University Press: Princeton, N.J.

16. U.S. Department of Energy, Technical Support Document: Energy Efficiency Program for Consumer Products and Commercial and Industrial Equipment: Residential Clothes Washers (Direct Final Rule) , Building Technologies Program, Editor. 2012: Washinton, D.C.

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