Vertical Integration and R&D Information Flow

The model considers an industry of two firms, a vertically integrated firm (U-D1) and an independent downstream firm (D2). The upstream division of the integrated firm, U, is a monopolist and produces an input which is essential for the production of the final goods.

Partially vertically integrated industry

For simplicity it is assumed that the input of firm U cannot be cheaply duplicated by firms who are denied access to it. U has no fixed costs, no capacity constraints and faces a constant marginal cost which is set to zero. D1 obtains the product from U at marginal cost, while the non-integrated downstream firm D2 obtains it at an endogenously determined wholesale price w.

In the first stage analysed, the firms simultaneously and independently choose their R&D effort levels.

Deriving from the representative consumer’s utility5, U-D1 and D2 face the following demand functions:

(1)

where q1 and q2 are the final good quantities of firms U-D1 and D2 and d is the degree of product differentiation.

The cost functions for firms U-D1 and D2 are:6

(2)

where x1 and x2 are the R&D investments of firm U-D1 and D2, respectively.

To include the effect of information flow into the model, it is assumed that the non-integrated downstream firm does not enjoy any spillovers and thus k is set equal to 0; whereas the integrated firm profits from spillovers (k>0) unless there is a ‘firewall’ (k=0).

Even in the absence of R&D investments the non-integrated firm faces costs w which are the wholesale price it has to pay in order to obtain the product from supplier U.

Concerning the R&D investments the model assumes a quadratic form of the cost of R&D:

(3)

This implies that the cost per unit of R&D increases with the size of the research level. The cost parameter µ represents a lower efficiency of the R&D expenditures.

In order to guarantee strictly positive quantities and R&D levels, in other words that the second order condition is satisfied the model assumes that the degree of product differentiation d is lower than ? where ? = 1 - (1 / 2µ).