A monopoly supplier of a good sells its product to two firms who are in turn monopolist in their respective markets. The first firm is F1, a seller...

A monopoly supplier of a good sells its product to two firms who are in turn monopolist in their respective markets. The first firm is F1, a seller of the good who faces a demand function of q=2-p. The second firm is F2, who faces a demand function of q=1-p for the same good. Assume that the supplier's marginal cost of producing good is constant and equal to 0.1, and he incurs no fixed cost. Should the monopoly vertically integrate with either firms? if yes, which firm? show your analysis.