210 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
In their experiments, a buyer and seller were paired. The seller chose price and the buyer chose quantity. In examining a vertical structure in which both the upstream and downstream
markets are monopolized, the choice space is essentially the same as in these bilateral bar- gaining experiments. The upstream firm chooses price, and the downstream firm, probably
taking final demand into consideration, indicates the quantity it wishes to purchase for that price. In the Fouraker and Siegel experiments, the pairs were randomly chosen, and each
subject had an anonymous partner. They examined the tendency for these pairs to be closer to the Bowley solution analogous to the double marginalization solution here or the Pareto
optimal solution analogous to the integrated solution. The Bowley solution was supported in their treatment with incomplete information and repeated play and with complete infor-
mation when the payoffs were split equally at the Bowley solution. The results are somewhat mixed when there is complete information, repeated play, and the payoffs are split equally
at the Pareto optimal solution. Several of the pairs found the Pareto solution under these conditions.
The monopolymonopoly experiments discussed here are very similar to Fouraker and Siegel’s treatment with incomplete information and repeated play with unequal payoffs at
the Bowley solution. However, the market structure with competition in the downstream markets is a variation of Fouraker and Siegel and predicts the Pareto Optimal solution with
the downstream firms earning only a normal profit. One important question is whether these downstream firms will be willing to earn 0 accounting profit or will they be able to cooperate
in some significant way in order to raise their profits?
2. Experimental design
The basic assumptions of Spengler’s theory are as follows. The upstream firm is as- sumed to choose a contract which the downstream firms either takes or leaves. This
contract consists only of an upstream price. The downstream firms, whose opportu- nity cost is normalized to 0, then chooses a price. After this, the consumers respond by
making their purchases. All firms are assumed to know demand. Each level of produc- tion is characterized by constant marginal costs, C
U
and C
D
, where the subscripts de- note upstream and downstream. The upstream firm knows both C
U
and C
D
, while the downstream firms knows only his own cost, C
D
. Assuming a linear demand, DP=a−bP, where a, b0, a downstream monopolist will choose P
D
to maxi- mize
5
D
= P
D
− P
U
− C
D
a − bP
D
, 1
giving a reaction function of P
D
= a + bP
U
+ bC
D
2b 2
The upstream monopolist will choose P
U
to maximize 5
U
= P
U
− C
U
a − bP
D
3
Y. Durham J. of Economic Behavior Org. 42 2000 207–229 211
subject to the downstream firm’s reaction function. The subgame perfect Nash equilibrium prices, quantity, and aggregate profit when both markets are monopolized are:
P
U
= a + bC
U
− bC
D
2b ,
P
D
= 3a + bC
D
− bC
U
4b ,
Q
U
= Q
D
= a − bC
D
− bC
U
4 ,
and 5
U
+ 5
D
= 3a − bC
U
− bC
D 2
16b .
4 An integrated firm would choose P to maximize
5 = P − C
U
− C
D
a − bP. 5
The integrated price, quantity, and profit are: P =
a + bC
D
+ bC
U
2b ,
Q = a − bC
D
− bC
U
2 ,
and 5 =
a − bC
D
− bC
U 2
2b .
6 If the downstream market is characterized by competition, then the downstream reaction
function will be P
D
= P
U
+ C
D
. The equilibrium then consists of the integrated final price, quantity, and total profit and an upstream price of
P
U
= a + bC
U
− bC
D
2b .
7 As long as abC
U
+ C
D
, the final price in the integrated structure or competitive down- stream structure is less than the final price in the monopolymonopoly structure, and profits
are higher. Using this linear structure for demand, the upstream monopolist will charge the same upstream price regardless of the structure downstream, so it is clear that the restriction
of quantity associated with a downstream monopolist will lower hisher profits.
In order to follow the assumptions of the theory as closely as possible, the institution used in these experimental markets is the posted-offer institution.
2
Smith 1981 found that the posted-offer institution is the pricing mechanism that is most supportive of the
monopoly price. It is also appropriate in this case because the downstream firm is assumed to be presented with a take-it-or-leave-it price.
The demand and cost conditions used for these experiments and the resulting price and quantity predictions are shown in Fig. 1. Also shown are the upstream residual demand
and the marginal revenue curves for both the upstream and downstream firm for the case in which both markets are monopolized. The downstream demand for each treatment was
a discrete form of the linear demand described previously with a=121 and b=0.2. All prices and costs during the experiments were denoted in experimental pesos. Downstream
marginal cost was constant at 100 pesos and upstream marginal cost was constant at 310 pesos. The residual demand that the upstream firm faces when the downstream market is
monopolized is the marginal revenue curve associated with the downstream demand minus
2
These experiments were hand-run with the aid of computerized buyers for the monopolycompetition experi- ments.
212 Y. Durham J. of Economic Behavior Org. 42 2000 207–229
Fig. 1. Underlying demand and cost conditions. Table 1
Price, quantity, and profit predictions
a
P
U
P
D
Q 5
U
5
D
MonopolyMonopoly 410
555 10
1040 490
MonopolyCompetition 405
505 20
1980 80
a
Prices and profits are in pesos. Profit figures include commissions but are prior to the subtraction of the lump sum payments of 520 for MM experiments and 1400 for MC experiments from the upstream subjects. Although
demand is linear, the discreteness causes upstream prices to vary between the two treatments. The actual predicted upstream price with a continuous demand would be 407.5 pesos.
the downstream marginal cost. A linear demand curve was used because it provided the cleanest marginal revenue curve to work with. With a continuous linear demand as well
as linear costs, theory predicts that the upstream firm will set the same price regardless of the downstream market structure. In the case of competition downstream, P
D
will be equal to downstream marginal cost or P
U
+ 100. Substituting P
D
= P
U
+ 100 into Eq. 3 yields
Eq. 7, the same P
U
as in the case of monopoly downstream.
3
In all of the experiments, both the upstream and downstream markets had a capacity of 54 units. In the competitive
case, three identical firms shared this capacity. The theoretical predictions for upstream and downstream prices, quantities, and profits for these designs can be found in Table 1.
Because the model assumes constant marginal costs, competitive firms earn zero eco- nomic profits in equilibrium. In order to assure that the subjects in the experiments did not
earn zero accounting profits, a commission of 4 pesos was paid to each subject whenever
3
Graphically, the upstream firm’s marginal revenue curve in the monopolycompetition case is the upstream firm’s demand curve in the monopolymonopoly case. Since MC is linear, MR=MC at double the quantity when
going from a monopolized downstream to a competitive downstream. Since MR divides the quantity demanded space in half when demand is linear, the price of the MR curve demand curve in the monopolymonopoly case
will be the same as the price off the demand curve in the monopolycompetition case when quantity is doubled.
Y. Durham J. of Economic Behavior Org. 42 2000 207–229 213
heshe sold a unit in both types of experiments. Price offers were restricted to being made in 5 peso increments to avoid a distortion in predictions stemming from this commission. The
only effect the commission had was to sharpen the prediction in the monopolymonopoly case. Because the theory predicts that the upstream firm will squeeze all of the profit out
of the downstream on the last unit, the commission provides an incentive to trade the last unit. Since prices could only be made in five peso increments, the upstream firm had no
way to extract the four peso commission from the downstream firm on the last unit. This is illustrated in Fig. 1. Marginal revenue equals marginal cost at 10 units for the upstream
firm. Upstream price would therefore be set at 410. Marginal cost for the downstream firm would be 410+100 or 510, causing marginal revenue to intersect marginal cost on the step
for the 10th unit. Therefore, the downstream firm would be indifferent between selling 9 units and 10 units. The 4 peso commission provides an incentive for the downstream firm
to sell this last unit, and the requirement that prices be in 5 peso increments prevents the upstream firm from extracting those 4 pesos from the downstream firm.
An exchange rate of 2.5 pesoscent was used for the monopolists in each experiment. An exchange rate of 0.25 pesoscent was used for the competitive firms since the competitive
firms were earning only commissions in equilibrium. In the monopolymonopoly exper- iments, the difference between downstream profits at the Nash prediction and the profits
at one unit below the prediction is only the 4 peso commission. The experiments were designed so that a subject’s indifference between choosing the predicted quantity and one
unit less would not involve a significant portion of the market. This, along with the linear demand curve, meant that the upstream monopolists in these markets would have earned
a great deal of money at the predicted prices. Using a large exchange rate would have flattened out the payoff function more than was felt suitable, so a lump sum payment was
taken from the upstream firm each period. Theoretically, this should not affect a subject’s maximizing choices. The lump sum payment was made small enough to allow for a wide
variety of choices and mistakes, so final payments to the monopolists still tended to be above average.
4
3. Experimental procedures
