Profit-Maximising Rigid Prices and Vertical Integration

Abstract

This article explores profit-maximising rigid pricing for a price-setting firm and relates the results to vertical integration, which is an important area of corporate strategy and antitrust policy. The setting of a profit-maximising rigid price is investigated in the face of a known distribution of short-run demand levels as a compromise between the flexible prices that would be appropriate in the short run at different levels of demand. The price and level of capacity are therefore set to maximise expected profits across varying levels of demand. With the help of computer simulations, it is shown that price rigidity increases the incentives for vertical integration, particularly where upstream production is capital intensive, due to the increased importance of rationing. The incentives will also be particularly strong for more efficient and more capital-intensive downstream production with low short-run marginal costs.

Key Words:

• Price Rigidity
• Vertical Integration
• Restraints
• Rationing
• Capacity

JEL classifications:

• L10
• L23
• D42
• D45

Acknowledgements

I am grateful to the journal’s anonymous referees for their help with this article.

Notes

1. $\frac{\mathit{\partial }E(\mathit{\pi })}{\mathit{\partial }{Q}_{cap}}=\left(\frac{\mathit{\partial }}{\mathit{\partial }{Q}_{cap}}\left({\int }_{q_{min}}^{Q_{cap}}f(q_t,P)q_{t}d{q}_t\right)+\frac{\mathit{\partial }}{\mathit{\partial }{Q}_{cap}}\left(\left(1-F(Q_{cap},P)\right)\right)Q_{cap}\right)\left(P-c_{prod}\right)-c_{cap}=\left(f(Q_{cap},P)Q_{cap}-f(Q_{cap},P)Q_{cap}+(1-F(Q_{cap},P))\right)\left(P-c_{prod}\right)-c_{cap}=\left(\left(1-F(Q_{cap},P\right)\right)\left(P-c_{prod}\right)-c_{cap}$