When a vertically integrated monopolist (VIM) is the only supplier of an input used by firms in a downstream market and competes with its rival in this downstream market, the VIM has to decide its downstream product price and its input price when the upstream market is not regulated. Since the rival must buy the input from the VIM in order to produce and sell its product, the pricing decisions of the VIM might raise the concern of refusals to deal or price squeeze. I fill the gap of the literature by showing that both the as-efficient competitor (AEC) and the protected profits benchmark (PPB) could suffer from over-deterrence risks when both markets are unregulated.