Economies of scale, natural monopoly, and imperfect competition in an experimental market.

• Author: Plott, Charles R.

1. Introduction

   This paper reports on the behavior of markets in which all agents have identical costs with economies of scale over the entire range of demand. Each firm, by choosing a larger scale of plant and a larger volume, can experience lower average cost. Thus, the markets are characterized by the fundamental technological property that has motivated decades of theorizing about natural monopoly and imperfect competition. The primary question posed by the research is whether or not a natural monopoly emerges and sets prices at monopoly levels, or whether the data are more closely approximated by some alternative model of imperfect competition, such as monopolistic competition, Cournot oligopoly, or contestable market theory.

   Some of the principle results of the experiments reported here can, in retrospect, be interpreted as having been anticipated by the pathbreaking work of Coursey, Isaac, Luke and Smith [1, 69-84], and by Coursey, Isaac, and Smith [2, 91-113]. While these previous experiments involved economic environments that were much less complicated than the one studied here, the tendencies previously observed are clearly present in the behaviors reported here. So, in a sense, the results reported here can be interpreted as a major extension of the previous results, as well as replication and robustness check.

   The similarities of experimental design with previous experiments rest on the facts of falling average cost and no barriers to entry that existed in all experiments. However, the number and nature of departures from the previous research are substantial. The markets studied here were much larger, so parameters took values in a more continuous manner. The experiments studied here involved two markets, so entry into the falling average cost market was accompanied by the opportunity cost of profits foregone in the alternative market. The alternative market was a computerized double auction which agents generally enjoy, so entry into the falling average cost market did not result from an attempt to relieve boredom, which one might have suspected played a role in previous studies. Agents entering the falling average cost market were required to make a choice of scale of plant that affected costs. Thus, the theory of cost minimization played an active role in developing models. This dimension was completely absent from previous experiments. Previous experiments used linear average costs that fell with volume until a capacity constraint was reached (within the range of demand) and then costs became vertical. Average costs in the experiments reported here were nonlinear and fell throughout the range of demand. In addition, the nonlinearities, scale economies, and demand were configured to create Cournot equilibria in the appropriate Cournot model of the environment. The Cournot equilibria were separated from the competitive (price equals average cost plus opportunity cost) equilibrium. In previous experiments the Cournot equilibrium was also the competitive equilibrium. The number of potential entrants used in previous experiments was small, ranging from two to four. In the experiments reported here, there were seven potential competitors. Briefly put, the choice of parameters for the experiments reported here was such that the economic environment was similar to those commonly found in the figures in economics textbooks.

2. Experimental Environment, Design and Procedures

   A total of three experiments were conducted. Subjects were students at the California Institute of Technology and summer interns at Caltech. Some of the subjects were experienced in the operation of electronic markets. As it turns out, the empirical tendencies that were observed in the experiments are so pronounced that only three experiments appear to be needed to answer the original question posed. Since the experiments are expensive in terms of time and money, a decision was made to limit the number of experiments to three. Given the behavior exhibited by the twenty-one people studied, the expectation that anything would be learned from additional replications seems too low to justify the cost.

   Each experiment consisted of 7 buyers and 7 sellers. Subjects with experience were placed in the more complex role of sellers. Two markets were created. They will be called market A and market B. The buyers could participate in both. Sellers could participate in either but not in both. In market A sellers had identical cost functions designed such that they were guaranteed a rent from participating in the market. The parameters were chosen such that in market A the rents per seller and the market price were (theoretically) independent of the number of sellers that chose to sell in that market. Market A was organized by a (computerized) double auction that fully occupied the attention of the sellers that chose to function in that market so they would not be motivated by boredom to enter market B.

   Market B was different. Sellers that chose to operate in market B made irrevocable decisions about scale of plant, the quantity that they would offer for sale and the price they would post. Thus, the market organization was the standard posted price environment in which commitments were private information until the market opened. The only difference was that a seller could choose to drop out of the market once the decisions of other sellers were public but before the market opened. The decisions to drop out were also private (revealed simultaneously) and irrevocable. The dropout decision served to limit losses to the opportunity cost of market A profits foregone, and reduced the probability that subject bankruptcies would disrupt the experiment. In market B all sellers had the same cost function. The cost function was characterized by economies of scale.

   In summary, the economic environment had the following properties:

   1. Participation in market B involved an opportunity cost because reasonably predictable rents could be gained from participation in market A.

   2. Participation in market A was "fun" in the sense that many people enjoy the speed and activity of the computerized double auction.

   3. Participation in market B could be done without exposure to a major out-of-pocket loss. Sellers could "drop out" if they expected volume to be less than was anticipated at the time that scale of plant was chosen.

   4. All transactions took place in a currency called francs. Each franc was converted to dollars at a rate of .0075 for buyers and .006 for sellers.

   The Market Environment

   A continuous approximation of market demands for markets A and B are contained in Figure 1. The equation for the continuous approximation of the market demand in market B is

   P = 1110 - 25x. (1)

   Individual parameters for the demanders are in Table 1. Each of seven demanders made money by participating in market A and in market B. Each buyer had the same redemption values in market A each period. That is, in market A both the market demand and the individual redemption values were constant over periods. In market B, the market demand was constant over periods but the redemption value of each individual changed from period to period. A fixed family of schedules was rotated among the individual demanders. The rotation schedule is contained in Plott, Sugiyama, and Elbaz [8]. The rotation convention was used because uncertainty about which model might be most accurate gave us little confidence in our ability to predict incomes of buyers. We wanted the income of all subject buyers to be sufficiently high to keep their interests. The rotation had a useful feature of removing dramatic asymmetries. Each of seven sellers had identical costs throughout the experiment. The fact that the costs were identical was not known by any agent in the markets. Each had the option of participating in either market A or in market B, but not in both. A seller that participated in market A used the cost schedule in Table I. For a single seller the graph of the (marginal) costs are included in Figure 1. As can be seen, the seller had two low cost units and then had constant cost afterwards for enough units to satisfy the entire demand.

   Table I. Individual Incentives Market A Market B Unit Demand(*) Costs(**) Market Demand(***) 1 1000 550 1085 2 1000 550 1060 3 1000 700 1035 4 400 700 1010 5 400 700 985 6 400 700 960 7 400 700 935 8 400 700 910 9 400 700 etc. 10 400 700 -25 each unit 11 400 700 -- 12 400 700 -- 13 400 700 -- 14 400 700 -- 15 400 700 -- 16 -- 17 -- 18 -- 19 * All buyer agents (00 through 06) had the same demand as listed here. ** All seller agents (07 through 13) had the same costs as listed here. *** Individual agents demand rotated each period Given these individual costs in market A, the market price (according to the competitive model) will be constant at 700 at all volumes near the demand (at 21 units) regardless of the number of suppliers in market A. As will be stated more clearly below, the equilibrium price will be near 700 and rents for all sellers in market A will be about 300 (2 units at 150 = 700 - 550 each) regardless of the number of other sellers in market A, as long as there are at least two.(1)

   The costs of all seven suppliers were the same for market B. Each subject had separate tables (in different colors) for marginal cost, average cost, and total cost. The total cost table is shown as Table II. As can be seen, costs depended upon both scale of plant and volume of sales.

   A continuous approximation to the underlying discrete parameter cost function has been useful in the development of behavioral predictions, as well as experimental design decisions. Figure 2 contains a graph of the long-run average cost curve in this continuous model, and also the short-run average costs for selected scales of plant. A continuous approximation of the market demand curve is imposed over the average cost for comparison.

   The formula for the competitive model is as follows. The...