Download Price discrimination Summary

How a Price-Discrimination Monopolist Reaches Equilibrium

We will find out how the price discriminating monopolist selling in two markets,
decides what price to charge in each market.

Assume that our firm is a manufacturing firm, selling its product on the home
and foreign markets.

We will also assume that our firm faces a downward sloping demand curve for
the product on both markets. In order to sell more our price will have to be
reduced.
Table 14.1 - Revenue Conditions in the home market for a price-discriminating
monopolist
Units of output
(Q)
1
2
3
4
5
Average revenue
(AR=P)
50
45
39
35
31
Total revenue
(TR= P x Q)
50
90
117
140
155
Marginal revenue
50
40
27
23
15
Table 14.2 - Revenue Conditions in the foreign market for a price-discriminating
monopolist
Units of output
(Q)
1
2
3
4
5

Average revenue
(AR=P)
42
38
32
28
25
Total revenue
(TR= P x Q)
42
76
96
112
125
Marginal revenue
42
34
20
16
13
If the firm produces one unit of output it is obvious that it will be supplied in
the home market where the selling price is 50 Euro, and not in the foreign
market where the selling is only 42 Euro.

If the firm’s total output is two units, one unit will be supplied to the home
market (at 50 Euro) and one unit to the foreign market (at 42 Euro) – this way
revenue is maximised at 92 Euro.
 If both units had been supplied to the home market, total revenue would
have been 90 Euro (two units at 45 Euro each).
 If both units had been supplied to the foreign market, total revenue
would have been 76 Euro (two units at 38 Euro each).
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
If the firm produces three units of output, how many should be sold in each
market?
 If all three units are sold at home, total revenue is 117 Euro (3 units at
39 Euro each)
 If all three units are sold abroad total revenue is 95 Euro (3 units at 32
Euro each)
 If we sell two units at home and one abroad, total revenue is 132 Euro (2
units at 45 Euro each and 1 at 42 Euro)
 If we sell one unit at home and two abroad, total revenue is 126 Euro (1
unit at 50 Euro and 2 at 38 Euro each)
 Therefore to maximise profits, we should sell two units at home and one
abroad.

If we look at marginal revenue on both markets would we arrive at the same
conclusion? So the firm is already selling one unit at home and one unit abroad
and is uncertain about where to sell the third unit:
 Selling the extra unit on the home market, marginal revenue would be 40
Euro, as it would be the second unit sold on this market.
 If the extra unit were sold abroad, marginal revenue would be 34 Euro, as
it would be the second unit sold on this market.
Table 14.3 – Allocation of output between markets and maximum revenue
attainable (based on revenue conditions shown in Tables 14.1 and 14.2)
Total output produced
1
2
3
4
5
6
7
8
Optimum allocation of
output
1 home
0 foreign
1 home
1 foreign
2 home
1 foreign
2 home
2 foreign
3 home
2 foreign
4 home
2 foreign
4 home
3 foreign
4 home
4 foreign
Maximum revenue
attainable (Euro)
50
92
132
166
193
216
236
252
2

14.3 – shows the optimum allocation of output between the two markets, and the
maximum revenue attainable for outputs in the range one to eight units.

Therefore, a condition for revenue maximisation is that marginal revenue in both
markets must be equal.
So far we have not mentioned cost. For profit maximisation (in any type of market) we
have already seen that the firm should produce that quantity where marginal revenue
equals marginal cost. Our basic rule for profit maximisation for a price discriminating
monopolist can now be finalised as follows:
A price-discriminating monopolist, in order to earn maximum profit, must produce
that quantity where marginal cost equals marginal revenue in the home market
equals marginal revenue in the foreign market.
Therefore, MC = MRh
=
MRf
Fig. 14.1 – Equilibrium for a price discriminating monopolist
Notice that we have drawn the home demand curve as a steeper graph than the foreign
one. This is usually the case since the firm’s demand is more likely to be inelastic at
home due to fewer competitors. This is why price charged on the home market is
higher than that charged abroad. However, marginal revenue on the home market is
the same as marginal revenue on the foreign market at the equilibrium position. Figure
14.1, (iii), shows the overall equilibrium position for the price discriminating monopolist
where MC=MR.
Profit maximisation occurs at the level of output Qt, where Qt = Qh + Qf.
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