Capacity choice with upstream investment

We consider a vertically related market with an upstream firm engaging in cost-reducing investment and n$$ n $$ downstream firms competing on quantity. We analyze the capacity choice by downstream firms. We find that input price decreases with production capacity if many downstream firms exist or the investment is efficient. More importantly, in the previous research, it is shown that the duopolistic downstream firms always choose undercapacity in a vertical market with an upstream firm. However, we find that overcapacity occurs in equilibrium if the number of downstream firms is large or the upstream investment is efficient.