Cross-holdings affect firms’ behavior in other vertically related markets. We consider a vertical market with two downstream firms and an upstream firm engaging in cost-reducing R&D. Since downstream cross-holdings weaken downstream competition, the upstream firm also decreases its investment. Hence, we find that as the degree of downstream cross-holdings increases, input price increases and investment level decreases. Although cross-holdings have this negative effect on downstream firms’ profits, they increase the downstream firms’ profits if the investment technology is inefficient.Finally, we show that with inefficient upstream investment, total surplus increases with
cross-holdings, while consumer surplus always decreases with cross-holdings.