Strategic Economics of Network Industries by Gottinger Hans

Author:Gottinger, Hans
Language: eng
Format: epub
Publisher: Nova Science Publishers, New York
Published: 2015-05-18T16:00:00+00:00

5.3. A SI M P L E M O D E L

We assume an economy with two firms, each one producing a differentiated good. There are two firms, h and w. Their initial technologies are represented by constant marginal production costs sh and sw. The first period innovation provides the cost-cutting technology s1. If allowed, the second period innovation offers the cost-cutting technology s. Here, technological progress is limited to be the cost-cutting technology, so called the process innovation. The firm that acquires new technology s1 or s can use it exclusively and produces its output at the cost of s1 or s, respectively. It is assumed, without loss of generality, that sh>sw>s1>s. At the beginning of each period, they compete for new technology s1 or s. Their competition for new technology is like a simple auction in which each firm proposes a bid which represents the maximum amount that firm will pay for the patent of the new technology and the highest bidder wins it. The winner pays -- as expense for buying the new technology --the maximum that the other firm would have paid in order to have the patent rather than not to have it. The loser does not owe anything.

The product market is specified by a differentiated duopoly of the Dixit (1979) type with linearity in demands assumed as follows:

qh = a % bph+cpw

qw = a % bpw+cph

where qi represents the demand for firm i and pi its price. It is further assumed that

a R 0 , b R c L 0 (1)

and

qh = a % bsh + cs L 0 (2) The goods are independent when c=0, while they are substitutes when c>0. When b=c, the goods are perfect substitutes. The assumption (2) implies that both firms are guaranteed to be active even after innovation.

After the race for new technology s1 or s, the firms compete in product market where the Bertrand competition is assumed. They set prices and the non-cooperative Nash equilibrium concept is adopted as the equilibrium in the product market.

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