Consider A Market For A Homogenous Good With Two Firms. Making The Appropriate Assumptions About Market Demand...

Consider A Market For A Homogenous Good With Two Firms. Making The Appropriate Assumptions About Market Demand,

b) Now suppose that one of the firms behaves as the Stackelberg quantity leader. Compare the equilibrium outcomes of Cournot verses Stackelberg

Stackelberg equilibriums act differently to Cournot equilibriums as Stackelberg equilibriums are asymmetrical. This creates a situation whereby the first firm makes a decision about output or price and the second firm has to react. Consequentially it creates different levels of income between the firms, unlike the Cournot equilibrium where profits are shared equally. Also, Stackelberg firms are less Pareto-inefficient, as they earn less net abnormal profits.

Unlike Cournot markets Stackelberg markets are not simultaneous but sequential, with one firm not making decisions based upon another firm’s future actions. Referring back to the example in part A consider that IBM is the first member if the computer industry. This enables it to be the quantity leader and set the level of output not based upon but inspite of Dell the new entrant. As a new entrant to the industry Dell is in no position to influence the market too significantly and has to react to the output decisions of IBM. This is because if Dell attempted to increase its output to match IBM’s levels it would risk lowering the unit price of computers too severely to justify entering the market. As a result, in a perfect Stackelberg model IBM would produce 50 units (based on there being 100 potential units in the market) and Dell 25 units, with both companies earning 25 abnormal profits per unit. This is different to the Cournot equilibrium where both firms would produce 33 1/3 units each, and earn 33 1/3 per unit as Game Theory requires a more even distribution of profits between companies.

Nash’s Game Theory explains how each firm has the ability to have high output or low output to influence profitability. We are taught that in order to maximise profits each firm will have to anticipate the other firms move. Both firms want to be in a position where they have high output but their rival produces a very low output, which would create 3 units of abnormal profits for the firm with the larger output but 0 for the firm with the lower output (see table below). If both firms happened to produce at low levels of output then they would earn the largest combined amounts of abnormal profits (4 units in the right table), as the price level would be driven up. However, if both firms attempted to produce at the highest level of output then they would create the lowest level of abnormal profits (2 in the right table), as the price level would be driven down.

Firm B
Output High Low
Firm A High (1,1) (3,0)
Low (0,3) (2,2)

Cournot equilibriums are more Pareto-inefficient than Stackelberg equilibriums. In Cournot equilibriums although both firms are choosing their second best options their abnormal profits combined are larger than Stackelberg equations. The Cournot example resembles that of both firms producing at lower levels, creating 4 units of abnormal profits. The Stackelberg equilibrium on the other hand would resemble the example of firm A (IBM) producing 3 units of abnormal profits but firm B (Dell) producing no units of abnormal profits. Consequently there would be one less unit of abnormal profits under Stackelberg than Cournot and therefore would be more Pareto efficient. The figures used in the second paragraph on the amount of abnormal profits per unit and the amount of units produced in each equilibrium show the Cournot equilibrium to create the value of 2222 2/9 abnormal profits, whereas the Stackelberg equilibrium would create the value of 1875, therefore the has been a greater loss of utility to the consumers under the Cournot equilibrium.

At equilibrium Stackelberg leaders produce more than Stackelberg followers, whereas in a Cournot duopoly both firms would produce and charge the same amount. However, a Cournot market is able to extract the most abnormal profits and is therefore the more Pareto-inefficient.

This piece was written by Jonathan McHugh in December 2004