A monopoly manufactures its product in two factories with marginal cost functions MC1(Q1) and Q1where is the quantity produced in the first factory and MC2(Q2) is the quantity manufactured in the second factory. The monopoly’s total output is Q= Q1+Q2. Use a graph or math to determine how much total output the monopoly produces and how much it produces at each factory. (Hint: Consider the cases where the factories have constant marginal costs—not necessarily equal—and where they have upward-sloping marginal cost curves.
Consider constant marginal cost and suppose the monopoly is facing a linear demand function with inverse demand function p = a − bQ. The monopoly will produce Q = (MC − a)/2b, where MC is the lower of two marginal costs at the factory with the lower MC, and zero units at the factory with the higher MC. Supposing that both factories have increasing marginal costs, the monopoly will produce at two factories Q1 and Q2 such that MC(Q1) = MC(Q2) = MR