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An empirical test of the effect of excess capacity in price setting, capacity-constrained supergames
International
Journal
of Industrial
Organization
7 (1989) 231-241.
North-Holland
AN EMPIRICAL TEST OF THE EFFECT OF EXCESS CAPACITY IN PRICE SETTING, CAPACITY-CONSTRAINED SUPERGAMES
David I. ROSENBAUM* University of Nebraska, Lincoln, NE 68588-0489, Final version
received
October
USA
1988
In a multi-period game, industry excess capacity may act to deter lirms from cheating on a non-cooperative oligopoly price. A model is developed that translates the deterrrent influence of excess capacity into predictions about the relationship between excess capacity and oligopoly price+ost margins. The model is tested with time-series data from the U.S. aluminum industry. Results are consistent with those predicted by the model.
1. Introduction
In a single period, price-setting game, one might expect firms with excess capacity to undercut a non-cooperative oligopoly price. In a multi-period, price-setting game with capacity constraints this may not occur. Significant industry excess capacity may act to deter undercutting by raising the potential future losses from retaliation in comparison to present gains. This paper uses data from the United States aluminum industry to test the proposition that the price-cutting outcome may not always occur. Oligopolists aware of the long-term effects of their own pricing behavior may be restrained from lowering their own prices in the face of significant industry excess capacity.’ This paper is divided into five sections. Section 2 contains a discussion of theoretical predictions as to the effect excess capacity has on price-cost margins in supergames with capacity constraints. A model is developed to test these predictions. Section 3 contains a brief description of the United States aluminum industry. The model developed in section 2 is modified slightly to accommodate characteristics peculiar to the industry. The data are *My thanks to Rob Masson, William Brock and Stephen Martin for their helpful comments. ‘Masson and Shannan (1982) show that across a sample of 26 industries, higher levels of excess capacity lead to higher pricesost margins. They do not, however, find support for the hypothesis that excess capacity is strategically created. 0167-7187/89/$3.50
0
1989, Elsevier Science
Publishers
B.V. (North-Holland)
D.1. Rosenbaum, Excess capacity in price-setting supergames
232
presented in’ section 4, and results are described conclusion follows in section 6. 2. Theoretical
in section
predictions on the effects of excess capacity capacity-constrained supergames
5. A general
in
In classical Bertrand theory, when demand shocks create excess capacity, firms are tempted to lower prices below established market levels in hopes of capturing greater portions of industry demand and increasing capacity utilization. Scherer (1980, p. 206) writes ‘[t]here is evidence that industries characterized by high overhead costs are particularly susceptible to pricing discipline breakdowns when a cyclical or secular decline in demand forces member firms to operate well below designed plant capacity. This tendency appears to be especially marked in industries . . . using highly capital intensive production processes.’ In most industries, the marginal cost function is positively sloped in the neighborhood of minimum average cost. Demand ‘shortfalls’ relative to production at minimum average cost generate excess capacity and widen the gap between price and marginal cost. This creates an incentive for firms to cut prices for any perceived marginal revenue. As long as firms cover their variable costs, they may be tempted to lower price in anticipation of increasing capacity utilization and profit.’ Firms, however, may be reluctant to offer pricing concessions in a multiperiod oligopoly setting where detection and retaliation may prevail. Firms are concerted with the effect their current pricing decision have on future profits. Once detection and retaliation occur, the ensuing price war may lead to little sales gains for individual firms and lower total revenues for all firms. Thus, in a supergame situation, while there may be an incentive to undercut, or defect on a non-cooperative oligopoly price, there is a deterrent as well. The incentive is an expected short-term increase in output due to a low firm price but high market price. The deterrent is retaliation by other firms and a low, long-term market price. The probability of detection, delay until retaliation occurs and extent of retaliation all determine whether defection is profitable. The literature contains several discussions on the determination of gains and losses associated with defecting in a non-cooperative oligopoly setting. 2This is a result from a typical neoclassical model. According to Peck (1961, pp. 85-88) a fixed factor production function makes the marginal cost curve in the aluminum industry flat almost until capacity is reached. Near capacity marginal cost does turn up as less-efficient capacity is brought into use. Hence over most output levels, since marginal costs do not decrease in excess capacity, the price cost margin does not increase in excess capacity. Returning to Scherer’s argument, however, when firms have a preponderance of fixed costs relative to variable costs, short term liquidity concerns may induce managers to reduce prices in hopes of gaining sales and covering more of their lixed costs.
D.I. Rosenbaum,
Excess capacity
in price-setting
supergames
233
[See Friedman (1971), Radner (1980), Rubenstein (1979), Abreu et al. (1986), Lambson (1984).] Brock and Scheinkman (1985) show that in a price-setting supergame with capacity constraints, the incentive to defect or cheat on a non-cooperative agreement depends on the number of firms in the industry and industry capacity. In non-capacity-constrained supergames, firms can expand to meet all demand at any given price. This creates potentially large incentives and deterrents to defecting on an oligopoly price. If one firm prices slightly below the oligopoly level it can capture all demand. A firm’s incentive to defect is the difference between its share of oligopoly profits and the profit from supplying the whole market at a slightly lower price. But if one firm can lower its price and capture all demand, others can do so as well. Thus, other firms can retaliate by lowering their prices to just below the defector’s price, and capturing the entire market for themselves. The loss of oligopoly profits acts as the deterrent to deviating from the oligopoly price. In a capacity-constrained supergame however, there are limits to how far output can expand and how far price can fall. While a firm can price slightly below the oligopoly level, it can at most increase its output to productive capacity. Therefore, the incentive to defect depends on how much excess capacity a firm has when pricing at the oligopoly level. If it has no excess capacity, there is little incentive to defect. As its excess capacity increases, so do the gains from cheating. While a firm’s incentive to cheat depends on its own excess capacity, the deterrent to cheating depends upon rivals’ excess capacity. Firms retaliate against a defector by lowering their own prices and increasing their own outputs. But they can only lower their prices to the point where demand equals industry capacity. The strongest retaliation firms can impose on a defector is production forever at full capacity. Hence, industry excess capacity at the oligopoly price acts as a proxy for the expected extent of deterrence oligopoly members may impose on a price defector.3 Low levels of industry excess capacity imply little deterrence. High levels imply significant deterrence. Brock and Scheinkman translate these incentives and deterrents into effects that excess capacity have on an equilibrium oligopoly price. They show that the maximum sustainable price and profit level vary with capacity. The preceding discussion leads to certain predictions as to the effect excess capacity has on price-cost margins in a price-setting capacity-constrained supergame. [Other literature on pricing in supergames includes Green and 3An appropriate measure of the extent of retaliation the industry can impose against a firm i might be ~j+iEXjl/~IN,,PRODj, where EX,, and PROD,, measure firm j’s absolute levels of excess capacity and production respectively. The worst retaliation the industry could impose on Iirm i depends on the relative exent of excess capacity available to all but firm i. Individual firm levels of excess capacity, however, are unavailable for the aluminum industry. Hence the use of an industry-wide proxy in the empirical work. If, however, levels of firm excess capacity, firm sizes, and retaliations are suff%ziently symmetric, the use of this proxy should not matter greatly.
D.I. Rosenbaum, Excess capacity in price-setting supergames
234
Porter (1984), Rotemberg and Saloner (1986), Iwand and Rosenbaum (1988).] If oligopolists react as the theory predicts, high levels of firm excess capacity should provide an incentive to reduce firm price-cost margins. Industry excess capacity on the other hand should help enforce oligopoly pricing and maintain price-cost margins. These predictions suggest an examination of price-cost margins using the following model:
(1) where PCMi, is firm i’s pricesost margin in period t, FXCi, is firm i’s excess capacity as a percentage of its own production in period t, and IXC, is industry excess capacity as a percentage of industry production in period t. According to supergame theory, /I1 should be negative. Higher levels of firm excess capacity increase the incentive to cheat on the oligopoly price. /I* on the other hand should be positive. Increments in industry excess capacity should deter cheating. Multiplying both sides of (1) by firm i’s share of industry production, and summing across the i firms provides (assuming the /Is are identical for all firms):
PCM, = u. + a,lXC,,
(2)
where PCM, is the industry price-cost margin in period t, IXC, is as defined above, and a1 =/Ii +/II. Estimating the model in eq. (2) would provide information on the combined coefficient, /Ii and f12. It would not allow identification of the individual coefficients. However, some estimate of their magnitudes could be obtained from the combined coefficient. If ai is negative, clearly p, has to be negative. /I2 could be positive, but smaller than /I1 in absolute value. If ai is positive, one could deduce that /I2 must be positive and larger in absolute value than pi. A third alternative is that a1 is equal to zero. This result has two interpretations. The first is that fil and /I2 are both zero. The second explanation may be that fir and jIZ are opposite in sign, but equal in magnitude. Hence, estimating eq. (2) may provide some information on the effect excess capacity has in price-setting, capacity-constrained supergames. 3. The aluminum
industry
This model can be applied to the United States primary aluminum ingot industry using two different data sets, one for the time period 1955 through 1975 and the other for 1967 through 1981. Aluminum ingot is a producer good. While there are different purities of ingot, output is homogeneous
D.I. Rosenbaum,
Excess
capacity
in price-setting
supergames
235
across producers for any given grade. While producers publish a list price for ingot, the transaction price has been known to fall below the list, once by more than 24 percent [Council on Wage and Price Stability (1976, pp. 117-120)]. From 1955 to 1981 the industry grew from 3 to 12 producers. Entry occurred in two predominant forms. Several entrants were large foreign aluminum producers seeking greater access to the North American market. These firms were established world producers that built aluminum reduction capacity in the U.S. Other entrants were U.S. metal producing firms either integrating back or expanding their product lines to include aluminum products as well. Nevertheless, entry barriers were still significant due to very high sunk costs, long lags between construction and production start-ups, and the difficulties of coordinating several integrated production stages. While short-run demand for ingot was inelastic, long-run demand was relatively elastic. [See Peck (1961, ch. 4).] Short-run demand consisted of firms already using aluminum as an input. Long-run demand consisted of current and potential future users. In the 1950s at least, aluminum producers were interested in keeping ingot prices low to attract new consumers. Therefore, ingot prices typically did not rise to short-run profit maximizing levels during periods of excess demand. Ingot is produced via a fixed factor production process. The process exhibits significant fixed costs. Estimates show that in various years, fixed cost comprised from 30 to 46 percent of total costs [Council on Wage and Price Stability, (1976, p. 29)J. There are also significant costs associated with closing down and restarting production facilities. These facts led to inventory accumulation among the primary producers in times of slack demand. Producers were willing to accumulate inventory that had a low marginal production cost and potentially high resale value rather than incur shutdown and start-up costs. There were, however, limits to inventory accumulation. The Council on Wage and Price Stability suggests two: a reluctance on the part of the producers to make excursions into capital markets to finance additional inventory accumulation, and projections of a slow recovery. [See Council on Wage and Price Stability, (1976, p. 137).] Large inventories may have two contrasting impacts on price-cost margins. On the one hand, inventories may act like industry excess capacity. Large industry inventories increase the extent of threatened retaliation and act to deter price cutting. On the other hand, large firm inventories increase the spread of between firm oligopoly output and maximum attainable sales. Additionally, when inventories approach maximum levels, firms may be tempted to cut prices and increase sales to avoid the high costs associated with shut-down and start-up. The deterrent effect of inventories, however, may be small in comparison to excess capacity’s deterrent effect. Inventories are a stock measure while
236
D.I. Rosenbaum, Excess capacity
in price-setting supergames
excess capacity is a flow. Since retaliation depends on the extent to which the future flow of output can increase in response to cheating, inventories probably have a qualitatively similar but quantitatively smaller influence in deterring cheating. On the other hand, the costs associated with carrying inventories and the very substantial cost associated with idling and restarting capacity may act to induce price cutting when inventories are high. Hence inventories have a negative impact on margins. The model in eq. (2) can be expanded to account for inventories. In this case: (3)
where IN V, is the level of inventories held relative to production for primary producers in period t. A negative a2 is expected and would support the hypothesis that firms are willing to cut prices when inventories are high. The model is augmented in two other respects. Oligopoly theory suggests that the price-cost margin should be responsive to the number of producers in the industry.4 More producers may make it harder to organize an oligopoly. Members may have a harder time detecting cheating with several sellers. In addition, firms may have different cost structures or divergent views on an optimal oligopoly price. Eq. (3) is therefore adjusted to include N,, the number of firms in period t, and a disturbance term is added:’ (4)
The final adjustment concerns potential simultaneity between price-cost margins and industry excess capacity. For a given short-run marginal cost curve, greater margins generate greater excess capacity. To get around this problem, industry excess capacity is instrumented via the following equation: IXC,=yo+y,%ACAP,+pZ~+y,%A~
GNP +y4%
f
f
As+c’. t
(5)
In eq. (5), ZXC, is industry excess capacity in period t, GNP is real GNP, is capacity, PROD is production, COM is industry cost of materials and WGE is industry wages. The first variable is the percentage change in capacity from period t - 1 to period t (measured as {CAP,- CAP,_ ,}/ CAP,_I). The second is a measure of demand relative to fixed capacity. If beginning-of-period capacity at time t is treated as a predetermined variable, CAP
4Froeb and Geweke (1987) examine the structure-performance link in the aluminum industry. They find that while the industry is competitive in the long run, structure (i.e., concentration) has a significant impact on short-run pricing. ‘Results were also generated using a capacity-based Hertindahl Index and three-firm concentration ratio in place of the number of firms. These results are described in a later section.
D.1. Rosenhaum, Excess capacity in price-setting super-games
231
then, controlling for demand, the larger the percentage increase in capacity, the greater excess capacity should be. This is especially true since capacity is typically incremented in large chunks. The third and fourth variables represent material costs and wage costs per unit of output and are measured as percentage changes from the previous year. Again with capacity as a predetermined variable, and controlling for demand, higher unit costs should lead to greater excess capacity. At first it seemed a measure of absolute cost per unit would be most useful in explaining excess capacity, but several problems arose. For instance, nominal costs should rise over time. With a twenty year time series, however, nominal cost per unit would be much higher in the last year than the first, but may have little impact in explaining excess capacity. Real values may be more reasonable, but it is unclear what would be the proper deflator. Also, higher unit costs in the long run may have little influence on excess capacity once the market adjusts. Therefore, the most reasonable variable measures shortrun changes in unit cost with a fixed capacity. The percentage change in unit cost from the previous year seems the best proxy for this variable.
4. Data The yearly industry price cost margin is derived from Census Bureau data. It is measured as industry value of shipments minus the sum of wages and cost of materials, all divided by value of shipments. Wages and materials represent variable costs. In effect, the price-cost margin reflects the margin between price and average variable cost. However, given the fixed proportions nature of the production process at all capacity levels [see Peck (1961)] average variable cost should be a reasonable proxy for marginal cost.6 Industry excess capacity is derived from yearly issues of Minerals Yearbook. Industry capacity is actual beginning of year capacity.’ Production is %ome caution may be necessary in interpreting this proxy when the industry is capacity constrained. Near the constraint, marginal cost and average variable cost are likely to diverge. Given the lixed factor production funciton, however, this divergence should not be too great. Another problem may arise when capacity is fully utilized. If demand is crossing the vertical rather than horizontal portion of the industry marginal cost curve (as posited by a lixed factor production function up to capacity), then as demand rises yet further, price may be expected to rise as well. In the sample used in this analysis, such a situation occurred in the mid 1960s. In 1964 and 1965, excess capacity fell to less than 1 percent of production. A dummy variable equal to 1 for these two years was included in the analysis. Its coefficient, however, was not statistically different from zero. This is not unreasonable given Peck’s (1961) repeated assertion that aluminum producers were cautious not to raise prices during periods of excess demand. They chose to keep prices stable and ration instead (frequently to the exclusion of small demanders). ‘Results using beginning of year capacity data in the instrumenting equation are shown in eq. (6). Results using end of year capacity data and an average of the two capacity measures were similar. The only significant differences involved the coefficient for percentage of new capacity. This coefficient was larger and significant above the 95 percent level when end of period data were used. Price-cost margin results were very similar using all three sets of instruments.
238
D.I. Rosenbaum,
Excess capacity
in price-setting
supergames
actual yearly production. Percentage industry excess capacity is measured as industry excess capacity (capacity minus production) divided by industry total production. Industry inventories are derived from two sources. From 1955 through 1975, inventories are measured as the year-end stocks of primary aluminum held by primary producers as a proportion of yearly production. This data is obtained from Minerals Yearbook. However, the Yearbook stopped publishing this particular data in 1975. Hence the time series using this measure of inventories is restricted to 21 observations. In 1967 the Census Bureau began reporting, in its Current Industrial Reports, inventories of all aluminum metal, including scraps, ingot, metal in process and finished products held by primary producers. Hence a second data set is developed for the years 1967 through 1981. Inventories in this data set are measured as Census inventories relative to production. Given the variety of alumimum products in this measure, it is less meaningful than measures of primary alumimum inventories alone. The correlation between the two inventory measures in years when both were available is 0.58. The Minerals Yearbook inventory figure averaged about 5 percent of production. The census figure averaged close to 50 percent of production. No attempt was made to use these two inventory measures to create one measure encompassing the time period of the entire sample. Real gross national product is obtained from several issues of the Statistical Abstract of the United States. 5. Results
Results from generalized least squares estimation of the excess capacity instrument equation using a Cochrane-Orcutt two-step procedure to correct for first-order autocorrelation (OLS Durbin-Watson = 1.0) are shown below. IXC = 0.566* +0.230x (2.34)
ACAP, - 1.624* s
(0.76)
+ 0.067% A z (0.288)
(-2.20)
f
+ 0.452% A WCE,, PROD,
’ (1.80)
p =0.8169* (7.4933), t-statistics in parentheses, R-square between observed and predicted values=0.5351,
(6)
D.I. Rosenbaum,
Excess capacity
Table
in price-setting
supergames
239
1
The effect of excess capacity, number of firms and inventories on aluminum ingot price-cost margins.”
Constant Excess capacity as percent of production’ Number of ftrms Inventories as percent of production N R2 R-squared between observed and nredicted
1955-1975
1967-1981
0.4632b (12.692) 0.0349 (0.3450) -0.0101’ ( - 2.4788) -0.5523’ (-2.7169) 21
0.7301 (7.7456) 0.2989“ (1.5866) - 0.0336 (- 3.6639) -0.1182 (-1.1031) 15 0.55
0.60
_
“t-statistic in parentheses. ‘Significant at 98% level using two tail test. ‘Significant at 95% level using two tail test. “Significant at 80% level using two tail test. ‘This variable is instrumented.
Durbin-Watson
statistic= 1.5718.
* = significant 95% using two-tailed t test. The coeflicients take the right signs but only short-run changes in demand are statistically significant. The same instrument results are used in the pricecost margin model for both the 1955-1975 and 1967-1981 samples. The samples are different only because of inventory measures. Estimation of the price-cost margin model for the 1955-1975 period using the excess capacity instrument revealed autocorrelation among the disturbance terms (Durbin-Watson statistic equal to 0.85). The model was reestimated for the early sample using a Cochrane-Orcutt two-step procedure to correct for first-order autocorrelation. The GLS Durbin-Watson statistic is 1.50. The estimated rho is equal to 0.56 and is significantly different from zero (t statistic equal to 3.09). GLS results for this time period are reported in table 1. OLS estimation of the model for the later period revealed no autocorrelation problem. (The Durbin-Watson statistic equals 1.59. A correction for first-order autocorrelation generated a statistically insignificant p equal to -0.003. GLS results were practically identical to OLS results.) Therefore, OLS results for the 1967-1981 period are reported in table 1 as well. Clearly inventory levels influence pricing decisions in the early period. Inventories of primary aluminum averaged 5 percent of production during the early period and varied from 1 percent of production to almost 13
240
D.I. Rosenbaum,
Excess capacity
in price-setting
supergames
percent. During the latter period inventories of all aluminum products averaged 51 percent of production and varied from 38 to 67 percent of production. (The inventory measure should be higher in the 1967-1981 period since it includes stocks of all aluminum, not just primary.) In the early period, each percentage point increase in inventories roughly translates into a five-tenths of one percent decline in the price+ost margin. (Inventories and margins are measured in percentage terms.) Apparently firms were willing to lower margins to avoid the sunk costs involved with closing and re-opening production facilities. The insignificant coefficient in the latter period may be due to the variety of types of aluminum and fabrications in the measure. The number of firms in the market influences margins as well. During the early period, the industry price-cost margin falls by 1 percent with the addition of each new firm. Through this influence alone, the margin should fall by 9 percent as the industry goes from 3 to 12 firms. During the latter period, the margin falls by more than 3 percent with the addition of a new firm.* The impact industry excess capacity has on price-cost margins during the 1955-1975 period is less easily interpreted. Excess capacity has a small coefficient that is statistically insignificant. Looking back at eq. (2), this coefficient measures the joint impact that firm and industry excess capacity have on price-cost margins. One interpretation of this result is that neither excess capacity measure influences pricing. Another, perhaps more plausible interpretation, is that the implicit coefficients are similar in magnitude and opposite in sign. Either interpretation would suggest that aluminum producers did not act as Bertrand oligopolists during periods of significant excess capacity. During the 1967-1981 period, excess capacity has a somewhat clearer impact on price+ost margins. The coefficient on excess capacity is positive and significant above the 80 percent level. This suggests that while the implicit coefftcient on firm excess capacity may be negative, the implicit coefficient on industry excess capacity is probably positive. In this period at least, industry excess capacity apparently does act to help maintain pricecost margins.g sHertindahl Index and three-firm concentration ratio results for the 1955-1975 period were similar to those in table 1 of the text. The coefficients on excess capacity were positive and insignificant. Both the Hertindahl Index and CR3 had positive coefftcients, although only the latter was significant above 95 percent. A one percent increase in inventories drove the pricecost margin down by about one-half of one percent. In the later period, however, results were much stronger using the alternate concentration measures. Market concentration using either measure had a positive and significant (at 99 percent level) impact on margins. The coefficient on excess capacity was approximately 0.4 in both equations and significant at the 99 percent level. Each percentage point increase in inventories reduced margins by almost 0.2 percent. ‘Price controls were implemented from 1971 through 1974. Omission of these years from either sample did not significantly change results.
D.I. Rosenbaum, Excess capacity in price-setting supergames
241
6. Conclusion
Supergame theory argues that the static Bertrand result does not necessarily apply in a repeated game situation. In a capacity-constrained, pricesetting supergame, price-cost margins can be maintained in the face of significant industry excess capacity. Excess capacity, which would motivate price cutting in a single-period game, also determines the extent of retaliation that can occur against defection in a repeated game. This theoretical prediction is tested using data from the American aluminum ingot market. The results conform to the theoretical predictions. They can be interpreted as showing that industry excess capacity can bolster a non-cooperative oligopoly price. References Abreu, Dilip, David Pearce and Ennio Stacchetti, 1986, Optimal cartel equilibria with imperfect monitoring, Journal of Economic Theory 39,251-269. Brock, William A. and Jose A. Scheinkman, 1985, Price setting supergames with capacity constraints, Review of Economic Studies 52, 371-382. Council on Wage and Price Stability, 1976, Aluminum prices 1974-1975 (Government Printing Oftice, Washington, DC). Friedman, James, 1971, A non-cooperative equilibrium for supergames, Review of Economic Studies 28, 1-12. Froeb, Luke and John Geweke, 1987, Long run competition in the U.S. aluminum industry, International Journal of Jndustrial Organization 5, 67-78. Green, Edward J. and Robert H. Porter, 1984, Noncooperative collusion under imperfect price information, Econometrica 52, 87-100. Iwand, Thomas and David I Rosenbaum, 1988, Cyclical pricing in supergames with capacity constraints, University of Nebraska Working paper no. 88-4. Lambson, Val E., 1984, Self-enforcing collusion in large dynamic markets, Journal of Economic Theory 34, 282-291. Peck, Merton J., 1961, Competition in the aluminum industry: 1945-1958 (Harvard University Press, Cambridge, MA). Masson, Robert T. and Joseph Shannan, 1982, Excess capacity and limit pricing: An empirical test, Economica 53, 365-378. Radner. R.. 1980. Collusive behavior in non-coooerative eusilon eauilibria of olinooolies with - . long but finite lives, Journal of Economic Theory 22, 138-l-54. 1 Rotemberg, Julio J. and Garth Saloner, 1986, A supergame theoretic model of price wars during booms, American Economic Review 76, 390407. Rubenstein, A., 1979, Equilibrium in supergames with the overtaking criterion, Journal of Economic Theory 21, 1-9. Scherer, F.M., 1980, Industrial market structure and economic performance, 2nd ed. (Houghton Mitllin, Boston, MA). U.S. Bureau of the Census, various years, Current industrial reports (Government Printing Oflice, Washington, DC). U.S. Bureau of the Census, various years, Statistical abstract of the United States (Government Printing Office, Washington, DC). U.S. Department of the Interior, various years, Minerals yearbook (Government Printing Ofhce, Washington, DC).
Journal
of Industrial
Organization
7 (1989) 231-241.
North-Holland
AN EMPIRICAL TEST OF THE EFFECT OF EXCESS CAPACITY IN PRICE SETTING, CAPACITY-CONSTRAINED SUPERGAMES
David I. ROSENBAUM* University of Nebraska, Lincoln, NE 68588-0489, Final version
received
October
USA
1988
In a multi-period game, industry excess capacity may act to deter lirms from cheating on a non-cooperative oligopoly price. A model is developed that translates the deterrrent influence of excess capacity into predictions about the relationship between excess capacity and oligopoly price+ost margins. The model is tested with time-series data from the U.S. aluminum industry. Results are consistent with those predicted by the model.
1. Introduction
In a single period, price-setting game, one might expect firms with excess capacity to undercut a non-cooperative oligopoly price. In a multi-period, price-setting game with capacity constraints this may not occur. Significant industry excess capacity may act to deter undercutting by raising the potential future losses from retaliation in comparison to present gains. This paper uses data from the United States aluminum industry to test the proposition that the price-cutting outcome may not always occur. Oligopolists aware of the long-term effects of their own pricing behavior may be restrained from lowering their own prices in the face of significant industry excess capacity.’ This paper is divided into five sections. Section 2 contains a discussion of theoretical predictions as to the effect excess capacity has on price-cost margins in supergames with capacity constraints. A model is developed to test these predictions. Section 3 contains a brief description of the United States aluminum industry. The model developed in section 2 is modified slightly to accommodate characteristics peculiar to the industry. The data are *My thanks to Rob Masson, William Brock and Stephen Martin for their helpful comments. ‘Masson and Shannan (1982) show that across a sample of 26 industries, higher levels of excess capacity lead to higher pricesost margins. They do not, however, find support for the hypothesis that excess capacity is strategically created. 0167-7187/89/$3.50
0
1989, Elsevier Science
Publishers
B.V. (North-Holland)
D.1. Rosenbaum, Excess capacity in price-setting supergames
232
presented in’ section 4, and results are described conclusion follows in section 6. 2. Theoretical
in section
predictions on the effects of excess capacity capacity-constrained supergames
5. A general
in
In classical Bertrand theory, when demand shocks create excess capacity, firms are tempted to lower prices below established market levels in hopes of capturing greater portions of industry demand and increasing capacity utilization. Scherer (1980, p. 206) writes ‘[t]here is evidence that industries characterized by high overhead costs are particularly susceptible to pricing discipline breakdowns when a cyclical or secular decline in demand forces member firms to operate well below designed plant capacity. This tendency appears to be especially marked in industries . . . using highly capital intensive production processes.’ In most industries, the marginal cost function is positively sloped in the neighborhood of minimum average cost. Demand ‘shortfalls’ relative to production at minimum average cost generate excess capacity and widen the gap between price and marginal cost. This creates an incentive for firms to cut prices for any perceived marginal revenue. As long as firms cover their variable costs, they may be tempted to lower price in anticipation of increasing capacity utilization and profit.’ Firms, however, may be reluctant to offer pricing concessions in a multiperiod oligopoly setting where detection and retaliation may prevail. Firms are concerted with the effect their current pricing decision have on future profits. Once detection and retaliation occur, the ensuing price war may lead to little sales gains for individual firms and lower total revenues for all firms. Thus, in a supergame situation, while there may be an incentive to undercut, or defect on a non-cooperative oligopoly price, there is a deterrent as well. The incentive is an expected short-term increase in output due to a low firm price but high market price. The deterrent is retaliation by other firms and a low, long-term market price. The probability of detection, delay until retaliation occurs and extent of retaliation all determine whether defection is profitable. The literature contains several discussions on the determination of gains and losses associated with defecting in a non-cooperative oligopoly setting. 2This is a result from a typical neoclassical model. According to Peck (1961, pp. 85-88) a fixed factor production function makes the marginal cost curve in the aluminum industry flat almost until capacity is reached. Near capacity marginal cost does turn up as less-efficient capacity is brought into use. Hence over most output levels, since marginal costs do not decrease in excess capacity, the price cost margin does not increase in excess capacity. Returning to Scherer’s argument, however, when firms have a preponderance of fixed costs relative to variable costs, short term liquidity concerns may induce managers to reduce prices in hopes of gaining sales and covering more of their lixed costs.
D.I. Rosenbaum,
Excess capacity
in price-setting
supergames
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[See Friedman (1971), Radner (1980), Rubenstein (1979), Abreu et al. (1986), Lambson (1984).] Brock and Scheinkman (1985) show that in a price-setting supergame with capacity constraints, the incentive to defect or cheat on a non-cooperative agreement depends on the number of firms in the industry and industry capacity. In non-capacity-constrained supergames, firms can expand to meet all demand at any given price. This creates potentially large incentives and deterrents to defecting on an oligopoly price. If one firm prices slightly below the oligopoly level it can capture all demand. A firm’s incentive to defect is the difference between its share of oligopoly profits and the profit from supplying the whole market at a slightly lower price. But if one firm can lower its price and capture all demand, others can do so as well. Thus, other firms can retaliate by lowering their prices to just below the defector’s price, and capturing the entire market for themselves. The loss of oligopoly profits acts as the deterrent to deviating from the oligopoly price. In a capacity-constrained supergame however, there are limits to how far output can expand and how far price can fall. While a firm can price slightly below the oligopoly level, it can at most increase its output to productive capacity. Therefore, the incentive to defect depends on how much excess capacity a firm has when pricing at the oligopoly level. If it has no excess capacity, there is little incentive to defect. As its excess capacity increases, so do the gains from cheating. While a firm’s incentive to cheat depends on its own excess capacity, the deterrent to cheating depends upon rivals’ excess capacity. Firms retaliate against a defector by lowering their own prices and increasing their own outputs. But they can only lower their prices to the point where demand equals industry capacity. The strongest retaliation firms can impose on a defector is production forever at full capacity. Hence, industry excess capacity at the oligopoly price acts as a proxy for the expected extent of deterrence oligopoly members may impose on a price defector.3 Low levels of industry excess capacity imply little deterrence. High levels imply significant deterrence. Brock and Scheinkman translate these incentives and deterrents into effects that excess capacity have on an equilibrium oligopoly price. They show that the maximum sustainable price and profit level vary with capacity. The preceding discussion leads to certain predictions as to the effect excess capacity has on price-cost margins in a price-setting capacity-constrained supergame. [Other literature on pricing in supergames includes Green and 3An appropriate measure of the extent of retaliation the industry can impose against a firm i might be ~j+iEXjl/~IN,,PRODj, where EX,, and PROD,, measure firm j’s absolute levels of excess capacity and production respectively. The worst retaliation the industry could impose on Iirm i depends on the relative exent of excess capacity available to all but firm i. Individual firm levels of excess capacity, however, are unavailable for the aluminum industry. Hence the use of an industry-wide proxy in the empirical work. If, however, levels of firm excess capacity, firm sizes, and retaliations are suff%ziently symmetric, the use of this proxy should not matter greatly.
D.I. Rosenbaum, Excess capacity in price-setting supergames
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Porter (1984), Rotemberg and Saloner (1986), Iwand and Rosenbaum (1988).] If oligopolists react as the theory predicts, high levels of firm excess capacity should provide an incentive to reduce firm price-cost margins. Industry excess capacity on the other hand should help enforce oligopoly pricing and maintain price-cost margins. These predictions suggest an examination of price-cost margins using the following model:
(1) where PCMi, is firm i’s pricesost margin in period t, FXCi, is firm i’s excess capacity as a percentage of its own production in period t, and IXC, is industry excess capacity as a percentage of industry production in period t. According to supergame theory, /I1 should be negative. Higher levels of firm excess capacity increase the incentive to cheat on the oligopoly price. /I* on the other hand should be positive. Increments in industry excess capacity should deter cheating. Multiplying both sides of (1) by firm i’s share of industry production, and summing across the i firms provides (assuming the /Is are identical for all firms):
PCM, = u. + a,lXC,,
(2)
where PCM, is the industry price-cost margin in period t, IXC, is as defined above, and a1 =/Ii +/II. Estimating the model in eq. (2) would provide information on the combined coefficient, /Ii and f12. It would not allow identification of the individual coefficients. However, some estimate of their magnitudes could be obtained from the combined coefficient. If ai is negative, clearly p, has to be negative. /I2 could be positive, but smaller than /I1 in absolute value. If ai is positive, one could deduce that /I2 must be positive and larger in absolute value than pi. A third alternative is that a1 is equal to zero. This result has two interpretations. The first is that fil and /I2 are both zero. The second explanation may be that fir and jIZ are opposite in sign, but equal in magnitude. Hence, estimating eq. (2) may provide some information on the effect excess capacity has in price-setting, capacity-constrained supergames. 3. The aluminum
industry
This model can be applied to the United States primary aluminum ingot industry using two different data sets, one for the time period 1955 through 1975 and the other for 1967 through 1981. Aluminum ingot is a producer good. While there are different purities of ingot, output is homogeneous
D.I. Rosenbaum,
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capacity
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supergames
235
across producers for any given grade. While producers publish a list price for ingot, the transaction price has been known to fall below the list, once by more than 24 percent [Council on Wage and Price Stability (1976, pp. 117-120)]. From 1955 to 1981 the industry grew from 3 to 12 producers. Entry occurred in two predominant forms. Several entrants were large foreign aluminum producers seeking greater access to the North American market. These firms were established world producers that built aluminum reduction capacity in the U.S. Other entrants were U.S. metal producing firms either integrating back or expanding their product lines to include aluminum products as well. Nevertheless, entry barriers were still significant due to very high sunk costs, long lags between construction and production start-ups, and the difficulties of coordinating several integrated production stages. While short-run demand for ingot was inelastic, long-run demand was relatively elastic. [See Peck (1961, ch. 4).] Short-run demand consisted of firms already using aluminum as an input. Long-run demand consisted of current and potential future users. In the 1950s at least, aluminum producers were interested in keeping ingot prices low to attract new consumers. Therefore, ingot prices typically did not rise to short-run profit maximizing levels during periods of excess demand. Ingot is produced via a fixed factor production process. The process exhibits significant fixed costs. Estimates show that in various years, fixed cost comprised from 30 to 46 percent of total costs [Council on Wage and Price Stability, (1976, p. 29)J. There are also significant costs associated with closing down and restarting production facilities. These facts led to inventory accumulation among the primary producers in times of slack demand. Producers were willing to accumulate inventory that had a low marginal production cost and potentially high resale value rather than incur shutdown and start-up costs. There were, however, limits to inventory accumulation. The Council on Wage and Price Stability suggests two: a reluctance on the part of the producers to make excursions into capital markets to finance additional inventory accumulation, and projections of a slow recovery. [See Council on Wage and Price Stability, (1976, p. 137).] Large inventories may have two contrasting impacts on price-cost margins. On the one hand, inventories may act like industry excess capacity. Large industry inventories increase the extent of threatened retaliation and act to deter price cutting. On the other hand, large firm inventories increase the spread of between firm oligopoly output and maximum attainable sales. Additionally, when inventories approach maximum levels, firms may be tempted to cut prices and increase sales to avoid the high costs associated with shut-down and start-up. The deterrent effect of inventories, however, may be small in comparison to excess capacity’s deterrent effect. Inventories are a stock measure while
236
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in price-setting supergames
excess capacity is a flow. Since retaliation depends on the extent to which the future flow of output can increase in response to cheating, inventories probably have a qualitatively similar but quantitatively smaller influence in deterring cheating. On the other hand, the costs associated with carrying inventories and the very substantial cost associated with idling and restarting capacity may act to induce price cutting when inventories are high. Hence inventories have a negative impact on margins. The model in eq. (2) can be expanded to account for inventories. In this case: (3)
where IN V, is the level of inventories held relative to production for primary producers in period t. A negative a2 is expected and would support the hypothesis that firms are willing to cut prices when inventories are high. The model is augmented in two other respects. Oligopoly theory suggests that the price-cost margin should be responsive to the number of producers in the industry.4 More producers may make it harder to organize an oligopoly. Members may have a harder time detecting cheating with several sellers. In addition, firms may have different cost structures or divergent views on an optimal oligopoly price. Eq. (3) is therefore adjusted to include N,, the number of firms in period t, and a disturbance term is added:’ (4)
The final adjustment concerns potential simultaneity between price-cost margins and industry excess capacity. For a given short-run marginal cost curve, greater margins generate greater excess capacity. To get around this problem, industry excess capacity is instrumented via the following equation: IXC,=yo+y,%ACAP,+pZ~+y,%A~
GNP +y4%
f
f
As+c’. t
(5)
In eq. (5), ZXC, is industry excess capacity in period t, GNP is real GNP, is capacity, PROD is production, COM is industry cost of materials and WGE is industry wages. The first variable is the percentage change in capacity from period t - 1 to period t (measured as {CAP,- CAP,_ ,}/ CAP,_I). The second is a measure of demand relative to fixed capacity. If beginning-of-period capacity at time t is treated as a predetermined variable, CAP
4Froeb and Geweke (1987) examine the structure-performance link in the aluminum industry. They find that while the industry is competitive in the long run, structure (i.e., concentration) has a significant impact on short-run pricing. ‘Results were also generated using a capacity-based Hertindahl Index and three-firm concentration ratio in place of the number of firms. These results are described in a later section.
D.1. Rosenhaum, Excess capacity in price-setting super-games
231
then, controlling for demand, the larger the percentage increase in capacity, the greater excess capacity should be. This is especially true since capacity is typically incremented in large chunks. The third and fourth variables represent material costs and wage costs per unit of output and are measured as percentage changes from the previous year. Again with capacity as a predetermined variable, and controlling for demand, higher unit costs should lead to greater excess capacity. At first it seemed a measure of absolute cost per unit would be most useful in explaining excess capacity, but several problems arose. For instance, nominal costs should rise over time. With a twenty year time series, however, nominal cost per unit would be much higher in the last year than the first, but may have little impact in explaining excess capacity. Real values may be more reasonable, but it is unclear what would be the proper deflator. Also, higher unit costs in the long run may have little influence on excess capacity once the market adjusts. Therefore, the most reasonable variable measures shortrun changes in unit cost with a fixed capacity. The percentage change in unit cost from the previous year seems the best proxy for this variable.
4. Data The yearly industry price cost margin is derived from Census Bureau data. It is measured as industry value of shipments minus the sum of wages and cost of materials, all divided by value of shipments. Wages and materials represent variable costs. In effect, the price-cost margin reflects the margin between price and average variable cost. However, given the fixed proportions nature of the production process at all capacity levels [see Peck (1961)] average variable cost should be a reasonable proxy for marginal cost.6 Industry excess capacity is derived from yearly issues of Minerals Yearbook. Industry capacity is actual beginning of year capacity.’ Production is %ome caution may be necessary in interpreting this proxy when the industry is capacity constrained. Near the constraint, marginal cost and average variable cost are likely to diverge. Given the lixed factor production funciton, however, this divergence should not be too great. Another problem may arise when capacity is fully utilized. If demand is crossing the vertical rather than horizontal portion of the industry marginal cost curve (as posited by a lixed factor production function up to capacity), then as demand rises yet further, price may be expected to rise as well. In the sample used in this analysis, such a situation occurred in the mid 1960s. In 1964 and 1965, excess capacity fell to less than 1 percent of production. A dummy variable equal to 1 for these two years was included in the analysis. Its coefficient, however, was not statistically different from zero. This is not unreasonable given Peck’s (1961) repeated assertion that aluminum producers were cautious not to raise prices during periods of excess demand. They chose to keep prices stable and ration instead (frequently to the exclusion of small demanders). ‘Results using beginning of year capacity data in the instrumenting equation are shown in eq. (6). Results using end of year capacity data and an average of the two capacity measures were similar. The only significant differences involved the coefficient for percentage of new capacity. This coefficient was larger and significant above the 95 percent level when end of period data were used. Price-cost margin results were very similar using all three sets of instruments.
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D.I. Rosenbaum,
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supergames
actual yearly production. Percentage industry excess capacity is measured as industry excess capacity (capacity minus production) divided by industry total production. Industry inventories are derived from two sources. From 1955 through 1975, inventories are measured as the year-end stocks of primary aluminum held by primary producers as a proportion of yearly production. This data is obtained from Minerals Yearbook. However, the Yearbook stopped publishing this particular data in 1975. Hence the time series using this measure of inventories is restricted to 21 observations. In 1967 the Census Bureau began reporting, in its Current Industrial Reports, inventories of all aluminum metal, including scraps, ingot, metal in process and finished products held by primary producers. Hence a second data set is developed for the years 1967 through 1981. Inventories in this data set are measured as Census inventories relative to production. Given the variety of alumimum products in this measure, it is less meaningful than measures of primary alumimum inventories alone. The correlation between the two inventory measures in years when both were available is 0.58. The Minerals Yearbook inventory figure averaged about 5 percent of production. The census figure averaged close to 50 percent of production. No attempt was made to use these two inventory measures to create one measure encompassing the time period of the entire sample. Real gross national product is obtained from several issues of the Statistical Abstract of the United States. 5. Results
Results from generalized least squares estimation of the excess capacity instrument equation using a Cochrane-Orcutt two-step procedure to correct for first-order autocorrelation (OLS Durbin-Watson = 1.0) are shown below. IXC = 0.566* +0.230x (2.34)
ACAP, - 1.624* s
(0.76)
+ 0.067% A z (0.288)
(-2.20)
f
+ 0.452% A WCE,, PROD,
’ (1.80)
p =0.8169* (7.4933), t-statistics in parentheses, R-square between observed and predicted values=0.5351,
(6)
D.I. Rosenbaum,
Excess capacity
Table
in price-setting
supergames
239
1
The effect of excess capacity, number of firms and inventories on aluminum ingot price-cost margins.”
Constant Excess capacity as percent of production’ Number of ftrms Inventories as percent of production N R2 R-squared between observed and nredicted
1955-1975
1967-1981
0.4632b (12.692) 0.0349 (0.3450) -0.0101’ ( - 2.4788) -0.5523’ (-2.7169) 21
0.7301 (7.7456) 0.2989“ (1.5866) - 0.0336 (- 3.6639) -0.1182 (-1.1031) 15 0.55
0.60
_
“t-statistic in parentheses. ‘Significant at 98% level using two tail test. ‘Significant at 95% level using two tail test. “Significant at 80% level using two tail test. ‘This variable is instrumented.
Durbin-Watson
statistic= 1.5718.
* = significant 95% using two-tailed t test. The coeflicients take the right signs but only short-run changes in demand are statistically significant. The same instrument results are used in the pricecost margin model for both the 1955-1975 and 1967-1981 samples. The samples are different only because of inventory measures. Estimation of the price-cost margin model for the 1955-1975 period using the excess capacity instrument revealed autocorrelation among the disturbance terms (Durbin-Watson statistic equal to 0.85). The model was reestimated for the early sample using a Cochrane-Orcutt two-step procedure to correct for first-order autocorrelation. The GLS Durbin-Watson statistic is 1.50. The estimated rho is equal to 0.56 and is significantly different from zero (t statistic equal to 3.09). GLS results for this time period are reported in table 1. OLS estimation of the model for the later period revealed no autocorrelation problem. (The Durbin-Watson statistic equals 1.59. A correction for first-order autocorrelation generated a statistically insignificant p equal to -0.003. GLS results were practically identical to OLS results.) Therefore, OLS results for the 1967-1981 period are reported in table 1 as well. Clearly inventory levels influence pricing decisions in the early period. Inventories of primary aluminum averaged 5 percent of production during the early period and varied from 1 percent of production to almost 13
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supergames
percent. During the latter period inventories of all aluminum products averaged 51 percent of production and varied from 38 to 67 percent of production. (The inventory measure should be higher in the 1967-1981 period since it includes stocks of all aluminum, not just primary.) In the early period, each percentage point increase in inventories roughly translates into a five-tenths of one percent decline in the price+ost margin. (Inventories and margins are measured in percentage terms.) Apparently firms were willing to lower margins to avoid the sunk costs involved with closing and re-opening production facilities. The insignificant coefficient in the latter period may be due to the variety of types of aluminum and fabrications in the measure. The number of firms in the market influences margins as well. During the early period, the industry price-cost margin falls by 1 percent with the addition of each new firm. Through this influence alone, the margin should fall by 9 percent as the industry goes from 3 to 12 firms. During the latter period, the margin falls by more than 3 percent with the addition of a new firm.* The impact industry excess capacity has on price-cost margins during the 1955-1975 period is less easily interpreted. Excess capacity has a small coefficient that is statistically insignificant. Looking back at eq. (2), this coefficient measures the joint impact that firm and industry excess capacity have on price-cost margins. One interpretation of this result is that neither excess capacity measure influences pricing. Another, perhaps more plausible interpretation, is that the implicit coefficients are similar in magnitude and opposite in sign. Either interpretation would suggest that aluminum producers did not act as Bertrand oligopolists during periods of significant excess capacity. During the 1967-1981 period, excess capacity has a somewhat clearer impact on price+ost margins. The coefficient on excess capacity is positive and significant above the 80 percent level. This suggests that while the implicit coefftcient on firm excess capacity may be negative, the implicit coefficient on industry excess capacity is probably positive. In this period at least, industry excess capacity apparently does act to help maintain pricecost margins.g sHertindahl Index and three-firm concentration ratio results for the 1955-1975 period were similar to those in table 1 of the text. The coefficients on excess capacity were positive and insignificant. Both the Hertindahl Index and CR3 had positive coefftcients, although only the latter was significant above 95 percent. A one percent increase in inventories drove the pricecost margin down by about one-half of one percent. In the later period, however, results were much stronger using the alternate concentration measures. Market concentration using either measure had a positive and significant (at 99 percent level) impact on margins. The coefficient on excess capacity was approximately 0.4 in both equations and significant at the 99 percent level. Each percentage point increase in inventories reduced margins by almost 0.2 percent. ‘Price controls were implemented from 1971 through 1974. Omission of these years from either sample did not significantly change results.
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6. Conclusion
Supergame theory argues that the static Bertrand result does not necessarily apply in a repeated game situation. In a capacity-constrained, pricesetting supergame, price-cost margins can be maintained in the face of significant industry excess capacity. Excess capacity, which would motivate price cutting in a single-period game, also determines the extent of retaliation that can occur against defection in a repeated game. This theoretical prediction is tested using data from the American aluminum ingot market. The results conform to the theoretical predictions. They can be interpreted as showing that industry excess capacity can bolster a non-cooperative oligopoly price. References Abreu, Dilip, David Pearce and Ennio Stacchetti, 1986, Optimal cartel equilibria with imperfect monitoring, Journal of Economic Theory 39,251-269. Brock, William A. and Jose A. Scheinkman, 1985, Price setting supergames with capacity constraints, Review of Economic Studies 52, 371-382. Council on Wage and Price Stability, 1976, Aluminum prices 1974-1975 (Government Printing Oftice, Washington, DC). Friedman, James, 1971, A non-cooperative equilibrium for supergames, Review of Economic Studies 28, 1-12. Froeb, Luke and John Geweke, 1987, Long run competition in the U.S. aluminum industry, International Journal of Jndustrial Organization 5, 67-78. Green, Edward J. and Robert H. Porter, 1984, Noncooperative collusion under imperfect price information, Econometrica 52, 87-100. Iwand, Thomas and David I Rosenbaum, 1988, Cyclical pricing in supergames with capacity constraints, University of Nebraska Working paper no. 88-4. Lambson, Val E., 1984, Self-enforcing collusion in large dynamic markets, Journal of Economic Theory 34, 282-291. Peck, Merton J., 1961, Competition in the aluminum industry: 1945-1958 (Harvard University Press, Cambridge, MA). Masson, Robert T. and Joseph Shannan, 1982, Excess capacity and limit pricing: An empirical test, Economica 53, 365-378. Radner. R.. 1980. Collusive behavior in non-coooerative eusilon eauilibria of olinooolies with - . long but finite lives, Journal of Economic Theory 22, 138-l-54. 1 Rotemberg, Julio J. and Garth Saloner, 1986, A supergame theoretic model of price wars during booms, American Economic Review 76, 390407. Rubenstein, A., 1979, Equilibrium in supergames with the overtaking criterion, Journal of Economic Theory 21, 1-9. Scherer, F.M., 1980, Industrial market structure and economic performance, 2nd ed. (Houghton Mitllin, Boston, MA). U.S. Bureau of the Census, various years, Current industrial reports (Government Printing Oflice, Washington, DC). U.S. Bureau of the Census, various years, Statistical abstract of the United States (Government Printing Office, Washington, DC). U.S. Department of the Interior, various years, Minerals yearbook (Government Printing Ofhce, Washington, DC).