Two transport monopolies in neighboring countries find themselves in competition on a shared market after deregulation. The demand function for transport is given as yD(p) = 8p and the cost functions for the two firms, B and S, are CTB(y) = 1/2y^2 and CTS(y) = 1/4y^2. The firms will determine their optimal production quantities by considering the other's reaction, and the market will reach an equilibrium with certain quantities, price, and profits for each firm.

1. Cournot-style oligopoly
The political authorities of Borduria and Syldavia decide to open up their market for
transport, which until then had been governed by a monopoly.
The monopolies of these two countries find themselves in competition on a single common
market (we will assume
that the costs of entering this market are too high for producers other than these two
companies have an interest in entering it).
The preferences of consumers in these two countries for transport services are identical and the
aggregate demand function is:
yD(p) = 8 p, with p, the transport price.
The cost functions of monopolies B and S are:
CTB(y) = 1 /2 y2 and CTS(y) = 1 4 /y2 .
It is assumed that neither firm has a strategic advantage over the other.
1. Determine the reaction functions of these two firms.
2. Calculate the quantities produced, the selling price and the profits of the two firms at
equilibrium.
3. Represent this balance graphically.
4. Calculate the total amount of transport in this duopoly situation. Deduct the surplus that the
consumers of this market as well as the collective surplus.