FEP - Working Papers - Universidade do Porto

4.2 Consumers’ surplus
From the point of view of consumers, competition between department stores is the most
favorable scenario. Prices are lower than in the other scenarios, and transportation costs
are minimized. It is not so straigtforward to compare the case of competition between
two shopping malls (lower transportation costs) with the case of competition between a
shopping mall and a department store (lower prices).
The total consumers’ surplus is given by: 12
CS = ˜x (V − PL) + (1 − ˜x) (V − PR) −
where V = � n
i=1 Vi.
� ˜x
0
tx dx −
� 1
˜x
t (1 − x) dx,
Let CSDD, CSMM and CSDM denote the consumers’ surplus in the three different
scenarios: (DD) competition between two department stores; (MM) competition between
two shopping malls; and (DM) competition between a department store and a shopping
mall.
Recall that when the mode of retail is the same in both extremes of the city, the price
of the basket of goods is equal at both extremes. As a result, the indifferent consumer is
located at the middle of the city and the total transportation cost is minimized. When
there are two department stores, the price of the basket is t. When there are two shopping
malls, the basket costs nt. Consequently:
and
CSDD = 1
� 1
1
2
(V − t) + (V − t) − t x dx − t
2 2 0
CSMM = 1
� 1
1
2
(V − nt) + (V − nt) − t x dx − t
2 2 0
� 1
1
2
� 1
1
2
(1 − x) dx = V − 5
4 t
(1 − x) dx = V −
�
n + 1
�
t.
4
12 Recall that the “one stop shopping” condition holds. Then, consumers located at [0, ˜x[ purchase all
goods at x = 0, while consumers located at ]˜x, 1] make all purchases at x = 1.
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