Agents in Economic Markets and Games
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a cost of £10 for every good produced. Thus the cost function of the firm i
can be given as
cost i = 10 × q i
(6.2)
where q i is the quantity produced by firm i.
Therefore having established demand and quantities produced by the firms,
the market price is given by
P market = P zero × (Q max − Q)
(6.3)
where P zero is the starting price of the product, assumed to be £1 in the
experiment.
Given this price, the profit of each firm i can be calculated by
P rof it i = (P market × q i ) − (cost i × q i )
(6.4)
FIGURE 6.8: Firm reaction curves in a duopoly model. A duopoly market
is a market with only two acting firms. Adapted from [5].
Using these mathematical notations (Equations 6.1-6.4) graphs can be
plotted to show exactly where the equilibrium will occur. Figure 6.8 depicts
the reaction curves of two firms competing in a duopoly market. If Firm 1 ’s
production is zero, Firm 2 can dominate the market by producing quantity
equal to the demand. In this case, Firm 1 and 2, the demand in the system
is 72. When Firm 1 starts producing, Firm 2 should reduce its output as
the total quantity being produced becomes more than the demand. If there
is too much of the product, this reduces its sales and Firm 2 will suffer high
loss. Note, that all products have to be sold in the same iteration. If the total
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a cost of £10 for every good produced. Thus the cost function of the firm i
can be given as
cost i = 10 × q i
(6.2)
where q i is the quantity produced by firm i.
Therefore having established demand and quantities produced by the firms,
the market price is given by
P market = P zero × (Q max − Q)
(6.3)
where P zero is the starting price of the product, assumed to be £1 in the
experiment.
Given this price, the profit of each firm i can be calculated by
P rof it i = (P market × q i ) − (cost i × q i )
(6.4)
FIGURE 6.8: Firm reaction curves in a duopoly model. A duopoly market
is a market with only two acting firms. Adapted from [5].
Using these mathematical notations (Equations 6.1-6.4) graphs can be
plotted to show exactly where the equilibrium will occur. Figure 6.8 depicts
the reaction curves of two firms competing in a duopoly market. If Firm 1 ’s
production is zero, Firm 2 can dominate the market by producing quantity
equal to the demand. In this case, Firm 1 and 2, the demand in the system
is 72. When Firm 1 starts producing, Firm 2 should reduce its output as
the total quantity being produced becomes more than the demand. If there
is too much of the product, this reduces its sales and Firm 2 will suffer high
loss. Note, that all products have to be sold in the same iteration. If the total