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Entry, capacity, investment and oligopolistic pricing: A model of the U.S. fiberglass insulation industry
soao-Econ Plon so, Vol 13. pp 191-195 0 Pergamon Press Ltd. 1979 Printed m Great Main
w38421/79/oKwo191/$02
wo
ENTRY, CAPACITY, INVESTMENT AND OLIGOPOLISTIC PRICING: A MODEL OF THE U.S. FIBERGLASS INSULATION INDUSTRY NOEL D. URIt Department of Energy, Office of Energy Source Analysis, Oil and Gas Analysis Division, Washington, DC 20461, U.S.A. (Received
24 October
1978)
Abstract-In this paper, a model is developed that suggests that entry into an industry selling a relatively homogeneous product can be deterred by investment decisions. The model characteristics are related to the institutional structure of the fiberglass insulation’industry in the United States with the conclusion that the behavior of the industry closely emulates that behavior predicted by the analysis.
In a recent paper, Michael Spence[l] argues that entry in an industry selling a relatively homogeneous product is likely to be affected by the relation between demand and industry capacity. Further, he suggests that entry can be deterred by investment decisions (one of which is capacity) and that the investment approach to entry allows for a unified treatment of entry in the homogeneous and differentiated product cases. The basic idea is that an industry will carry excess capacity to deter entry. As a result, price will exceed the limit price, and production will be inefficient. The threat of entry effectively places a lower bound on capacity. In this respect, the threat of entry is similar in its effects to a constraint on the industry’s rate of return. Spence develops his entire analysis devoid of any reference to specific examples (with the exception of a brief, undocumented, allusion to exclusive dealerships). In the present paper, this approach of Spence will be used to explain the structure and behavior of the fiberglass insulation industry in the United States and to shed light on the recent insulation shortages. In order to accomplish this, some background on the industry, as it is presently structured, is needed. BACKGROUND
The U.S. fiberglass insulation industry consists of three firms: Owens-Coming Fiberglas; Certain-Teed; and Johns-Manville. They accounted for approx. 50, 25 and 25%, respectively, of a total industry sales amounting to 472 million dollars in 1976. Owens-Corning is undisputedly the market leader [2]. Further, the existance of the few firms and the fact that fiberglass insulation effectively sets the prices for rock wool and cellulose insulation suggests that aggregate insulation industry prices depend importantly upon the three large fiberglass producers. (Total fiberglass insulation sales accounted for 76% of the total insulation market sales in 1976.) Thus, an explanation of the fiberglass insulation pricing behavior will, de facto, explain the pattern of the insulation industry’s pricing behavior. tThe views expressed are those of the author and do nol necessarily represent the policies of the department of energy or the views of other department of energy sti members. SSee Penoyar and Wiiiarns[3] and NAHB[41.
The demand for fiberglass insulation is divided into two separate components. The first component, that for retrofit, i.e. reinsulation of existing structures, is extremely variable, although it does appear to have a relatively stable component historically. The interesting aspect of this demand is that it is finite. That is, there are only so many homes to be retrofit (currently estimated to be between 25 and 47 million structures*) and once accomplished this component of demand will vanish from the market. The important factor explaining the demand for insulation in the retrofit market include, in addition to the price of insulation is the severity of the weather (Uri and Major[5]). Thus, much of the expansion of this component of current demand is the result of the abnormally cold weather in the winter of 1976-77 (in conjunction, of course, with rising energy prices). The second component of demand arises from new construction. New housing starts have been extremely variable although sustained high levels of housing starts are forecast through 1984 [6]. To the extent this is realized and because most new structures use fiberglass insulation, this component of the demand will continue to account for more than 50% of total sales. On the production side of the industry, some expansion in output has been realized through process improvements but the majority of it has resulted from the construction of new production facilities. The lead time involved in bringing a new plant on line is about two years although the process can be accelerated slightly if the demand conditions warrant it, witness Owens-Corning’s announcement that it will have additional capacity on line 4 months sooner than previously announced (Mabry 171). The demand for insulation is cyclical, closely following the level of new housing starts. Consequently, capacity utilization is highly dependent on this. Thus, during 1975 which witnessed a sharp decrease in housing starts, the industry capacity utilization was 55%. Additionally, the demand for insulation is seasonal, tied to the timing of new housing starts and the buying season for retrofit insulation. Both of these markets peak about October, with a low about March. Manufacturers attempt to keep finished product inventories at low levels. Owens-Corning, for example, maintains only a lo-day inventory under normal conditions. Fiberglass insulation is very 191
N.D. URI
192
bulky, requiring a substantial amount of warehouse space. Also, fiberglass material is compressed for storage and delivery and must be sold within six months or possibly it will undergo some distortion of shape. The foregoing information has been provided to give an indication of the institutional make-up of the fiberglass insulation industry. This information will be used in structuring a formal model to explain the industry behavior. It is to this we now turn. A MODEL OF THE FIBERGLAS INDUSTRY
The principle of this model is quite simple. It is that existing firms choose capacity in a strategic way designed to discourage entry. This strategic purpose is realized by holding “excess” capacity in the preentry period. This excess capacity permits firms to expand output and reduce price when entry is threatened, thereby reducing the prospective profits of the new entrant who operates on the residual demand curve to zero. Given that capacity is selected in this entry forestalling manner, existing firms choose preentry price and quantity so as to maximize profits. Before developing the model, it is convenient to introduce the following definitions and notation: let T denote the discrete time t where t=1,2,..., periods of equal length; y,, denote the quantity of fiberglass insulation demanded in the retrofit market in period t; yzl denote he quantity of fiberglass insulation demanded in the new construction market in period t; xt denote the supply of fiberglass insulation in period t: k, denote the production capacity of fiberglass insulation in period I; k. denote the production capacity of fiberglass insulation existing in the initial period: Z, denote the investment in production capacity of fiberglass insulation in period t; c,(x,) denotes the variable cost of production of fiberglass insulation in period t;t r, denotes the marginal cost per unit of capacity (capital cost) of the production of fiberglass insulation in peGod t; k, denote the minimum capacity needed to deter entry into the industry; j$ denote the total demand for fiberglass insulation in the retrofit market; 6, denote the portion of 8, satisfied in each period 1; and i denote the interest rate. Relying on the assumption that the demand functions for fiberglass insulation are known with certainty or are available in the certainty equivalence sense, the demand function for the retrofit market is given as PI, =fdY,t)
(1)
and for the new construction market it is given as P2r
=
f*(Yd
where
P,, and Pz,are the prices of fiberglass insulation in the retrofit market and new construction market, respectively, in period t.
The search for optimum demands, prices, and production is subject to several constraints as follows: (a) For each time period, the total quantity of fiberglass insulation demanded is less than or equal to the quantity supplied: (3)
Ylt + Y2r 5-G.
(b) For each time period, the total quantity of fiberglass insulation supplied must be less than or equal to the available capacity: X,5 k,.
(4)
(c) For each time period, production capacity of fiberglass insulation is less than or equal to the production capacity existing in the initial period plus the capacity additions in the first and subsequent periods: k,sko+
i Z, y=l
(d) In the aggregate, the demand for fiberglass insulation in the retrofit market is less than or equal to the sum of each period’s demand:
For convenience, it will be assumed that 7 2 T. (e) In each period, a portion of total fiberglass insulation demand is met: Ytt =
stg,.
(7)
ce
Notethat~&=landO
>
For convenience of exposition, the two constraints (6) and (7) will be combined into a single constraint as follows:
i=l
(f) For each period, following Spence ([l], p. 535), capacity is maintained above in particular level to deter entry: k; I k,.
(9)
Before proceeding, a number of points need to be clarified concerning the economic environment. (1) Additions to production capacity are looked upon as an average. To account for uncertainty or other contingencies a margin of spare capacity term could be included. (2) There is no discussion of terminal conditions. This does not preclude such discussions in a variant of the model. (3) This mode1 does not, as no model can, exhaustively explain industry behavior. It is simply agrued that the model presented here is suggestive of the observed behavior. PRODUCTIONOVER TIME
tNote costs.
that capacity is assumed to have no effect on variable
Under threat of entry, the industry maximizes profits, denoted by ?r(y,, y,, x, k, I), with respect to YI, YZ, x, k, and Z subject
to the constraints
(3)~(5),
(8) and (9).
193
Entry, capacity,investmentand oligopolisticpricing Before deriving the optimal conditions, it is instructive to look at the importance of constraint (9). Suppose the existing industry sets capacity at k, in any period t. Then when entry begins to occur, it can expand output to k, and lower price to p(t), (assuming a single price for the moment) within the time horizon required for entry. With respect to the time required for the installation of new capacity, the industry is on an equal footing with the potential entrant. It is assumed that the existing industry can hold the output x, = k, in the face of entry.? The demand left over to the entrant, i.e. the residual demand, is defined as follows: If the entrant supplied xt, total industry output is k, t xt. Therefore, price is p(& t xf), and this, regarded as a function of x*, is the inverse demand function facing the entrant. Entry is deterred if for a11x*, profits for the entrant are nonpositive; that is, for all x*
p,(k t x*)
c,w t
5 -
X?
r,, for a11t.
This simply says that price falls short of average cost for a11levels of production. It is clear that as k, increases, p(k tx*) falls for each x*. Indeed, for k sufficiently large, residual demand is zero. Consequently, there is a mini_mumlevel of k, which has previously been denoted as k, for which constraint IlO) holds. If the existing industry holds capacity at k, entry is deterred. Thus, constraint (9) is explained. With the objective of maximizing profits, the objective function of the problem may be characterized as n(y,, yz, x, k, I) =
2 ,
* * p2r +psr I$,, z,u”-‘Pw
k, 20
5 r,,
I, 2 0.
(20) (21)
The variable p:, can be interpreted as the cost to the industry for maintaining a capacity sufficient to deter entry. The variable p:, is the addition to cost when production capacity is totally utilized. That is, when capacity utilization is loo%, a positive cost is incurred. The variables prl and pzr have the obvious interpretations. The variable p:, is most interesting. It represents the additions to marginal revenue in the retrofit market due to the fact that demand is finite. Since relation (8) holds with equality, pz, will be positive. The most reasonable assumption in the anaiysis of the model presented is that both the retrofit and new construction demand for fiberglass insulation and hence the quantity supplied will be positive. Therefore, for
PT, = y~,fl(yd Pt
+
fdyd
+ C ~~-‘&.*qrp~~ t
(22a) (22b)
= Y*hTYlJ+f2(Y2r).
Given that constraint (8) is always binding, one can compute the difference in marginal revenues (defined as yiji’(y,,) tf,(yi,), i = 1,2). Thus, for marginal revenue in the two demand markets, MR, and MRz,
a'-'(Y1JI(Yd+ MRI,-MRzt Yzj2(Yzr)
xtct(xJ - dt)
-
where a’-’ = l/(1 t i)*-‘. Providing the demand functions are downward sloping and the aupply functions upwars sloping, the objective function is concave and the Kuhn-Tucker[8] conditions will give the necessary and sufficient conditions for optimality. Associating the dual variables or-‘p T,, CT’-‘p,*,, 6’pT,, d-‘p4*r, and g’-‘pT, with constraints (3)-(5), (8) and (9), respectively, and multiplying throughout by 6’ where appropriate, the Kuhn-Tucker conditions are
&O
Ylr+Y,*Ix,,
x,sk,,
=C
(11)
~‘-‘Sip:i-p.T,
(23)
which will be strictly positive provided the elasticity of demand is less in market one. (This is obvious since the first term on the right-hand side of eqn (23) will be greater than p t,.) Additions to production capacity are undertaken on the basis of a least-cost criterion. New capacity should be added in any period up to the point where the discounted sum of its quasi-rents equals the purchase price. Thus, if z, >o z, d-‘p
(12)
p:rzO
i
T,, = r,.
(24)
The quasi-rent of capacity in any period can be regarded as that part of the supply price set aside to cover depreciation and interest on capital. This is what Turvey(191, p. 291) calls amortization. If new production capacity is added in any period, marginal revenue in that period is equal to marginal cost of production plus amortization on the new plant less a cost sufficient to deter entry in the industry. Thus, if (16) YII > 0, ~2~ > 0, X, >
0, and Z,> 0 (and implicitly, k, > 0), (25)
then YzJ2’(Y21)
+ f2CY21)
‘P
:,,
Y2r 2 0
tThis is the assumptionof the limit price theory.
(18)
* p~r=MCttp:,-p:,
where MC is the marginal cost of production and is equal to the first two terms on the right-hand side of relation (19). If, on the other hand, it turns out to be the case that
194
N. D. URI
output does not fully utilize existing capacity (with the result that Z, = 0), then marginal revenue will just equal marginal cost less the entry deterring cost, with the result that output will be larger and price lower than what would be observed in the unconstrained (i.e. without constraint_ (9)) optimization problem. Further, once capacity k, is installed to deter entry, it may or may not be profitable to expand output to k. That depends on the structure of demand. As an aside, note that eqn (25) can be interpreted to mean that the present value of amortization equals the purchase price of new capacity. The issue to be emphasized is that the amount set aside for amortization varies from period to period depending on demand and perhaps is equal to zero in some periods. With demand varying, a constant proportion of capacity cost should not necessarily be recouped. Rather, capacity will be selected so that, over the life of the production capacity, capacity cost is just recouped. ANALYSIS OF THE MODEL
By casting the problem in the temporal dimension, the way has been open to handling many of the knotty problems with investment in capacity as well as the problems involved with price adjustment over time. The general principles of optimal pricing from the model can be summarized as follows: (1) Set prices (via marginal revenues) in accordance with the pattern of demand. Further, customers in the retrofit market need not be charged the same price as those in the new construction market. (2) Charge high prices when the quantity demanded rises above the level of production capacity. Thus, a fiberglass manufacturer can obtain a quasi-rent by charging a price in excess of that war-rented based on a marginal revenue equalling the various costs. (3) Capital costs are imputed to consumers to the extent their demand presses on production capacity. Thus, any increase in demand during a given period requiring the fiberglass industry to expand its generating capacity will result in a charge just sufficient to compensate for the increased cost associated with satisfying demand. (4) Lower marginal revenues by the cost incurred as a result of attempting to defer entry. Previously, it was argued that the fiberglass insulation industry has the institutional characteristics of the model outlined. The model then endeavored to explain the behavior of the industry with regard to pricing and entry deterrence. The next obvious question is just how well de facto, the model has accomplished its objective. It is to this question an answer is now provided. Because of the nature of the industry (e.g. composed of private corporations, no direct government regulation, and so on), data on the issues of interest are dillicult to obtain. Further, what data do exist are typically discretionary. In the present instance, only Owens-Corning Fiberglass has provided a sufficient amount of information to make any meaningful inferences. Consequently, the efficacy of the model will be based on that information source. The first thing to note is that Owens-Corning (O-C) does not sell directly to the final consumer. It sells to wholesale distributors or wholesale dealers. Additionally, it is able to differentiate between which of these dealers
sell to the retrofit market and which sell to the new construction market. Typically, O-C gives a discount of six sixes, i.e. 36%. to the wholesale customer. To some customers, however, it gives a discount of an additional six or fraction thereof (sometimes depending on the demand situation it is higher). It is not possible to objectively verify that wholesalers selling to the retrofit market are discriminated against price-wise. Extensive conversations, however, with O-C personnel indicate this is so. It has been indicated that wholesale dealers who supply contractors involved in constructing new houses on average receive a 6% additional discount over the price charged to wholesalers who supply fiberglass insulation to lumber yards and retail building material outlets. While O-C exercises no control over the price the first buyer (retail dealer) charges the next buyer (retail customer) in the distribution chain, the price markup by lumber yards and building materials outlets is characteristically greater than that occurring in the contractor market. The model, as developed, related marginal revenues in the two markets to costs and entry deterrences. In the preceeding paragraph, the discussion has been carried out in terms of prices. To translate the marginal revenue implications into prices some estimate of the demand elasticities for fiberglass insulation in the retrofit and the new construction market are needed. The only credible estimates available are those from Uri and Major [5]. In the retrofit market the elasticity is - 1.51 while in the new construction market it is estimated to be -1.78. Given these elasticities, the higher price in the retrofit market is consistent with the previous discussion. In the aggregate, one can conclude that the industry is pricing its product between the retrofit and new construction markets in a rational way. That is, higher in the former and lower in the latter. Now the issue of the maintenance of a sufficient capacity to deter entry is looked at. Data on capacity of utilization are available for Owens-Corning[lO]. These are presented in Table 1. The implications of the data are clear. Owens-Corning is maintaining spare capacity. While the purpose of such a margin can be justified on several grounds it is certainly consistent with the argument presented in this paper in light of the relatively short lead times required to add new capacity. Table 1. Utilization of fiberglass production Owens-Corning[lOI)
Year
capacity
(Source:
Rate of Capacity Utilization (annual)
1968
91
1969
90
1970
88
1971
92
1972
95
1973
95
1974
86
1975
69
1976
80
1977
92
Entry, capacity, investment and oligopolistic pricing CONCLUSIONS
In the foregoing analysis, a model has been developed that suggests that entry into an industry selling a relatively homogeneous product can be deterred by investment decisions. The model characteristics are related to the structure of the fiberglass insulation industry in the United States with the conclusion that the behavior of the industry closely emulates the behavior predicted by the analysis.
REFERENCES
I. A. M. Spence, Entry,capacity, investment and oligopolistic pricing. The Bell J. Econ. g(2). 534-544 (1977). 2. ICF Incorporated, Supply Response to Residential Insulation Retrofit Demand, ICF, Incorporated, Washington, June 1977. 3. W. Pennoyar and F. E. Williams, Surveys of U.S. residential
SEPSVol 13,No LC
195
capacity and projections for retrofitting U.S. housing inventory. Construction Rev. Aug./Sept. 1977.
insulation industry
4. National Association of Home Builders, The home insulation shortage, processed, Nov. 1977. 5. N. D. Uri and C. H. Major, The economics of energy conservation: the impact of federal building standards and tax credits on the demand for insulation. processed March 1978. 6. Data Resources, Incorporated (DRI), L&o Resources Review, Data Resources Incorporated, Cambridge, July 1977. 7. G. Maybry Statement before the senate subcommittee on inter-Governmental Relations, 2 Nov. 1977. 8. H. W. Kuhn and A. W. Tucker, Nonlinear programming. in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (Ed. by J. Neyman), pp. 481-492. University of Califormia Press, Berkeley (1951). 9. R. Turvey, Marginal cost. The Econ. J. LXXIX(314) 282-299. (1%9). 10. Owens-Corning Corp., Briefing Book, Owens-Corning Corporation, Toledo, Aug. 1977.
w38421/79/oKwo191/$02
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ENTRY, CAPACITY, INVESTMENT AND OLIGOPOLISTIC PRICING: A MODEL OF THE U.S. FIBERGLASS INSULATION INDUSTRY NOEL D. URIt Department of Energy, Office of Energy Source Analysis, Oil and Gas Analysis Division, Washington, DC 20461, U.S.A. (Received
24 October
1978)
Abstract-In this paper, a model is developed that suggests that entry into an industry selling a relatively homogeneous product can be deterred by investment decisions. The model characteristics are related to the institutional structure of the fiberglass insulation’industry in the United States with the conclusion that the behavior of the industry closely emulates that behavior predicted by the analysis.
In a recent paper, Michael Spence[l] argues that entry in an industry selling a relatively homogeneous product is likely to be affected by the relation between demand and industry capacity. Further, he suggests that entry can be deterred by investment decisions (one of which is capacity) and that the investment approach to entry allows for a unified treatment of entry in the homogeneous and differentiated product cases. The basic idea is that an industry will carry excess capacity to deter entry. As a result, price will exceed the limit price, and production will be inefficient. The threat of entry effectively places a lower bound on capacity. In this respect, the threat of entry is similar in its effects to a constraint on the industry’s rate of return. Spence develops his entire analysis devoid of any reference to specific examples (with the exception of a brief, undocumented, allusion to exclusive dealerships). In the present paper, this approach of Spence will be used to explain the structure and behavior of the fiberglass insulation industry in the United States and to shed light on the recent insulation shortages. In order to accomplish this, some background on the industry, as it is presently structured, is needed. BACKGROUND
The U.S. fiberglass insulation industry consists of three firms: Owens-Coming Fiberglas; Certain-Teed; and Johns-Manville. They accounted for approx. 50, 25 and 25%, respectively, of a total industry sales amounting to 472 million dollars in 1976. Owens-Corning is undisputedly the market leader [2]. Further, the existance of the few firms and the fact that fiberglass insulation effectively sets the prices for rock wool and cellulose insulation suggests that aggregate insulation industry prices depend importantly upon the three large fiberglass producers. (Total fiberglass insulation sales accounted for 76% of the total insulation market sales in 1976.) Thus, an explanation of the fiberglass insulation pricing behavior will, de facto, explain the pattern of the insulation industry’s pricing behavior. tThe views expressed are those of the author and do nol necessarily represent the policies of the department of energy or the views of other department of energy sti members. SSee Penoyar and Wiiiarns[3] and NAHB[41.
The demand for fiberglass insulation is divided into two separate components. The first component, that for retrofit, i.e. reinsulation of existing structures, is extremely variable, although it does appear to have a relatively stable component historically. The interesting aspect of this demand is that it is finite. That is, there are only so many homes to be retrofit (currently estimated to be between 25 and 47 million structures*) and once accomplished this component of demand will vanish from the market. The important factor explaining the demand for insulation in the retrofit market include, in addition to the price of insulation is the severity of the weather (Uri and Major[5]). Thus, much of the expansion of this component of current demand is the result of the abnormally cold weather in the winter of 1976-77 (in conjunction, of course, with rising energy prices). The second component of demand arises from new construction. New housing starts have been extremely variable although sustained high levels of housing starts are forecast through 1984 [6]. To the extent this is realized and because most new structures use fiberglass insulation, this component of the demand will continue to account for more than 50% of total sales. On the production side of the industry, some expansion in output has been realized through process improvements but the majority of it has resulted from the construction of new production facilities. The lead time involved in bringing a new plant on line is about two years although the process can be accelerated slightly if the demand conditions warrant it, witness Owens-Corning’s announcement that it will have additional capacity on line 4 months sooner than previously announced (Mabry 171). The demand for insulation is cyclical, closely following the level of new housing starts. Consequently, capacity utilization is highly dependent on this. Thus, during 1975 which witnessed a sharp decrease in housing starts, the industry capacity utilization was 55%. Additionally, the demand for insulation is seasonal, tied to the timing of new housing starts and the buying season for retrofit insulation. Both of these markets peak about October, with a low about March. Manufacturers attempt to keep finished product inventories at low levels. Owens-Corning, for example, maintains only a lo-day inventory under normal conditions. Fiberglass insulation is very 191
N.D. URI
192
bulky, requiring a substantial amount of warehouse space. Also, fiberglass material is compressed for storage and delivery and must be sold within six months or possibly it will undergo some distortion of shape. The foregoing information has been provided to give an indication of the institutional make-up of the fiberglass insulation industry. This information will be used in structuring a formal model to explain the industry behavior. It is to this we now turn. A MODEL OF THE FIBERGLAS INDUSTRY
The principle of this model is quite simple. It is that existing firms choose capacity in a strategic way designed to discourage entry. This strategic purpose is realized by holding “excess” capacity in the preentry period. This excess capacity permits firms to expand output and reduce price when entry is threatened, thereby reducing the prospective profits of the new entrant who operates on the residual demand curve to zero. Given that capacity is selected in this entry forestalling manner, existing firms choose preentry price and quantity so as to maximize profits. Before developing the model, it is convenient to introduce the following definitions and notation: let T denote the discrete time t where t=1,2,..., periods of equal length; y,, denote the quantity of fiberglass insulation demanded in the retrofit market in period t; yzl denote he quantity of fiberglass insulation demanded in the new construction market in period t; xt denote the supply of fiberglass insulation in period t: k, denote the production capacity of fiberglass insulation in period I; k. denote the production capacity of fiberglass insulation existing in the initial period: Z, denote the investment in production capacity of fiberglass insulation in period t; c,(x,) denotes the variable cost of production of fiberglass insulation in period t;t r, denotes the marginal cost per unit of capacity (capital cost) of the production of fiberglass insulation in peGod t; k, denote the minimum capacity needed to deter entry into the industry; j$ denote the total demand for fiberglass insulation in the retrofit market; 6, denote the portion of 8, satisfied in each period 1; and i denote the interest rate. Relying on the assumption that the demand functions for fiberglass insulation are known with certainty or are available in the certainty equivalence sense, the demand function for the retrofit market is given as PI, =fdY,t)
(1)
and for the new construction market it is given as P2r
=
f*(Yd
where
P,, and Pz,are the prices of fiberglass insulation in the retrofit market and new construction market, respectively, in period t.
The search for optimum demands, prices, and production is subject to several constraints as follows: (a) For each time period, the total quantity of fiberglass insulation demanded is less than or equal to the quantity supplied: (3)
Ylt + Y2r 5-G.
(b) For each time period, the total quantity of fiberglass insulation supplied must be less than or equal to the available capacity: X,5 k,.
(4)
(c) For each time period, production capacity of fiberglass insulation is less than or equal to the production capacity existing in the initial period plus the capacity additions in the first and subsequent periods: k,sko+
i Z, y=l
(d) In the aggregate, the demand for fiberglass insulation in the retrofit market is less than or equal to the sum of each period’s demand:
For convenience, it will be assumed that 7 2 T. (e) In each period, a portion of total fiberglass insulation demand is met: Ytt =
stg,.
(7)
ce
Notethat~&=landO
>
For convenience of exposition, the two constraints (6) and (7) will be combined into a single constraint as follows:
i=l
(f) For each period, following Spence ([l], p. 535), capacity is maintained above in particular level to deter entry: k; I k,.
(9)
Before proceeding, a number of points need to be clarified concerning the economic environment. (1) Additions to production capacity are looked upon as an average. To account for uncertainty or other contingencies a margin of spare capacity term could be included. (2) There is no discussion of terminal conditions. This does not preclude such discussions in a variant of the model. (3) This mode1 does not, as no model can, exhaustively explain industry behavior. It is simply agrued that the model presented here is suggestive of the observed behavior. PRODUCTIONOVER TIME
tNote costs.
that capacity is assumed to have no effect on variable
Under threat of entry, the industry maximizes profits, denoted by ?r(y,, y,, x, k, I), with respect to YI, YZ, x, k, and Z subject
to the constraints
(3)~(5),
(8) and (9).
193
Entry, capacity,investmentand oligopolisticpricing Before deriving the optimal conditions, it is instructive to look at the importance of constraint (9). Suppose the existing industry sets capacity at k, in any period t. Then when entry begins to occur, it can expand output to k, and lower price to p(t), (assuming a single price for the moment) within the time horizon required for entry. With respect to the time required for the installation of new capacity, the industry is on an equal footing with the potential entrant. It is assumed that the existing industry can hold the output x, = k, in the face of entry.? The demand left over to the entrant, i.e. the residual demand, is defined as follows: If the entrant supplied xt, total industry output is k, t xt. Therefore, price is p(& t xf), and this, regarded as a function of x*, is the inverse demand function facing the entrant. Entry is deterred if for a11x*, profits for the entrant are nonpositive; that is, for all x*
p,(k t x*)
c,w t
5 -
X?
r,, for a11t.
This simply says that price falls short of average cost for a11levels of production. It is clear that as k, increases, p(k tx*) falls for each x*. Indeed, for k sufficiently large, residual demand is zero. Consequently, there is a mini_mumlevel of k, which has previously been denoted as k, for which constraint IlO) holds. If the existing industry holds capacity at k, entry is deterred. Thus, constraint (9) is explained. With the objective of maximizing profits, the objective function of the problem may be characterized as n(y,, yz, x, k, I) =
2 ,
* * p2r +psr I$,, z,u”-‘Pw
k, 20
5 r,,
I, 2 0.
(20) (21)
The variable p:, can be interpreted as the cost to the industry for maintaining a capacity sufficient to deter entry. The variable p:, is the addition to cost when production capacity is totally utilized. That is, when capacity utilization is loo%, a positive cost is incurred. The variables prl and pzr have the obvious interpretations. The variable p:, is most interesting. It represents the additions to marginal revenue in the retrofit market due to the fact that demand is finite. Since relation (8) holds with equality, pz, will be positive. The most reasonable assumption in the anaiysis of the model presented is that both the retrofit and new construction demand for fiberglass insulation and hence the quantity supplied will be positive. Therefore, for
PT, = y~,fl(yd Pt
+
fdyd
+ C ~~-‘&.*qrp~~ t
(22a) (22b)
= Y*hTYlJ+f2(Y2r).
Given that constraint (8) is always binding, one can compute the difference in marginal revenues (defined as yiji’(y,,) tf,(yi,), i = 1,2). Thus, for marginal revenue in the two demand markets, MR, and MRz,
a'-'(Y1JI(Yd+ MRI,-MRzt Yzj2(Yzr)
xtct(xJ - dt)
-
where a’-’ = l/(1 t i)*-‘. Providing the demand functions are downward sloping and the aupply functions upwars sloping, the objective function is concave and the Kuhn-Tucker[8] conditions will give the necessary and sufficient conditions for optimality. Associating the dual variables or-‘p T,, CT’-‘p,*,, 6’pT,, d-‘p4*r, and g’-‘pT, with constraints (3)-(5), (8) and (9), respectively, and multiplying throughout by 6’ where appropriate, the Kuhn-Tucker conditions are
&O
Ylr+Y,*Ix,,
x,sk,,
=C
(11)
~‘-‘Sip:i-p.T,
(23)
which will be strictly positive provided the elasticity of demand is less in market one. (This is obvious since the first term on the right-hand side of eqn (23) will be greater than p t,.) Additions to production capacity are undertaken on the basis of a least-cost criterion. New capacity should be added in any period up to the point where the discounted sum of its quasi-rents equals the purchase price. Thus, if z, >o z, d-‘p
(12)
p:rzO
i
T,, = r,.
(24)
The quasi-rent of capacity in any period can be regarded as that part of the supply price set aside to cover depreciation and interest on capital. This is what Turvey(191, p. 291) calls amortization. If new production capacity is added in any period, marginal revenue in that period is equal to marginal cost of production plus amortization on the new plant less a cost sufficient to deter entry in the industry. Thus, if (16) YII > 0, ~2~ > 0, X, >
0, and Z,> 0 (and implicitly, k, > 0), (25)
then YzJ2’(Y21)
+ f2CY21)
‘P
:,,
Y2r 2 0
tThis is the assumptionof the limit price theory.
(18)
* p~r=MCttp:,-p:,
where MC is the marginal cost of production and is equal to the first two terms on the right-hand side of relation (19). If, on the other hand, it turns out to be the case that
194
N. D. URI
output does not fully utilize existing capacity (with the result that Z, = 0), then marginal revenue will just equal marginal cost less the entry deterring cost, with the result that output will be larger and price lower than what would be observed in the unconstrained (i.e. without constraint_ (9)) optimization problem. Further, once capacity k, is installed to deter entry, it may or may not be profitable to expand output to k. That depends on the structure of demand. As an aside, note that eqn (25) can be interpreted to mean that the present value of amortization equals the purchase price of new capacity. The issue to be emphasized is that the amount set aside for amortization varies from period to period depending on demand and perhaps is equal to zero in some periods. With demand varying, a constant proportion of capacity cost should not necessarily be recouped. Rather, capacity will be selected so that, over the life of the production capacity, capacity cost is just recouped. ANALYSIS OF THE MODEL
By casting the problem in the temporal dimension, the way has been open to handling many of the knotty problems with investment in capacity as well as the problems involved with price adjustment over time. The general principles of optimal pricing from the model can be summarized as follows: (1) Set prices (via marginal revenues) in accordance with the pattern of demand. Further, customers in the retrofit market need not be charged the same price as those in the new construction market. (2) Charge high prices when the quantity demanded rises above the level of production capacity. Thus, a fiberglass manufacturer can obtain a quasi-rent by charging a price in excess of that war-rented based on a marginal revenue equalling the various costs. (3) Capital costs are imputed to consumers to the extent their demand presses on production capacity. Thus, any increase in demand during a given period requiring the fiberglass industry to expand its generating capacity will result in a charge just sufficient to compensate for the increased cost associated with satisfying demand. (4) Lower marginal revenues by the cost incurred as a result of attempting to defer entry. Previously, it was argued that the fiberglass insulation industry has the institutional characteristics of the model outlined. The model then endeavored to explain the behavior of the industry with regard to pricing and entry deterrence. The next obvious question is just how well de facto, the model has accomplished its objective. It is to this question an answer is now provided. Because of the nature of the industry (e.g. composed of private corporations, no direct government regulation, and so on), data on the issues of interest are dillicult to obtain. Further, what data do exist are typically discretionary. In the present instance, only Owens-Corning Fiberglass has provided a sufficient amount of information to make any meaningful inferences. Consequently, the efficacy of the model will be based on that information source. The first thing to note is that Owens-Corning (O-C) does not sell directly to the final consumer. It sells to wholesale distributors or wholesale dealers. Additionally, it is able to differentiate between which of these dealers
sell to the retrofit market and which sell to the new construction market. Typically, O-C gives a discount of six sixes, i.e. 36%. to the wholesale customer. To some customers, however, it gives a discount of an additional six or fraction thereof (sometimes depending on the demand situation it is higher). It is not possible to objectively verify that wholesalers selling to the retrofit market are discriminated against price-wise. Extensive conversations, however, with O-C personnel indicate this is so. It has been indicated that wholesale dealers who supply contractors involved in constructing new houses on average receive a 6% additional discount over the price charged to wholesalers who supply fiberglass insulation to lumber yards and retail building material outlets. While O-C exercises no control over the price the first buyer (retail dealer) charges the next buyer (retail customer) in the distribution chain, the price markup by lumber yards and building materials outlets is characteristically greater than that occurring in the contractor market. The model, as developed, related marginal revenues in the two markets to costs and entry deterrences. In the preceeding paragraph, the discussion has been carried out in terms of prices. To translate the marginal revenue implications into prices some estimate of the demand elasticities for fiberglass insulation in the retrofit and the new construction market are needed. The only credible estimates available are those from Uri and Major [5]. In the retrofit market the elasticity is - 1.51 while in the new construction market it is estimated to be -1.78. Given these elasticities, the higher price in the retrofit market is consistent with the previous discussion. In the aggregate, one can conclude that the industry is pricing its product between the retrofit and new construction markets in a rational way. That is, higher in the former and lower in the latter. Now the issue of the maintenance of a sufficient capacity to deter entry is looked at. Data on capacity of utilization are available for Owens-Corning[lO]. These are presented in Table 1. The implications of the data are clear. Owens-Corning is maintaining spare capacity. While the purpose of such a margin can be justified on several grounds it is certainly consistent with the argument presented in this paper in light of the relatively short lead times required to add new capacity. Table 1. Utilization of fiberglass production Owens-Corning[lOI)
Year
capacity
(Source:
Rate of Capacity Utilization (annual)
1968
91
1969
90
1970
88
1971
92
1972
95
1973
95
1974
86
1975
69
1976
80
1977
92
Entry, capacity, investment and oligopolistic pricing CONCLUSIONS
In the foregoing analysis, a model has been developed that suggests that entry into an industry selling a relatively homogeneous product can be deterred by investment decisions. The model characteristics are related to the structure of the fiberglass insulation industry in the United States with the conclusion that the behavior of the industry closely emulates the behavior predicted by the analysis.
REFERENCES
I. A. M. Spence, Entry,capacity, investment and oligopolistic pricing. The Bell J. Econ. g(2). 534-544 (1977). 2. ICF Incorporated, Supply Response to Residential Insulation Retrofit Demand, ICF, Incorporated, Washington, June 1977. 3. W. Pennoyar and F. E. Williams, Surveys of U.S. residential
SEPSVol 13,No LC
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capacity and projections for retrofitting U.S. housing inventory. Construction Rev. Aug./Sept. 1977.
insulation industry
4. National Association of Home Builders, The home insulation shortage, processed, Nov. 1977. 5. N. D. Uri and C. H. Major, The economics of energy conservation: the impact of federal building standards and tax credits on the demand for insulation. processed March 1978. 6. Data Resources, Incorporated (DRI), L&o Resources Review, Data Resources Incorporated, Cambridge, July 1977. 7. G. Maybry Statement before the senate subcommittee on inter-Governmental Relations, 2 Nov. 1977. 8. H. W. Kuhn and A. W. Tucker, Nonlinear programming. in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (Ed. by J. Neyman), pp. 481-492. University of Califormia Press, Berkeley (1951). 9. R. Turvey, Marginal cost. The Econ. J. LXXIX(314) 282-299. (1%9). 10. Owens-Corning Corp., Briefing Book, Owens-Corning Corporation, Toledo, Aug. 1977.