Question: Suppose that a Monopolist faces a demand curve of P=10-Q and operates two factories. Total Costs at the respective factories are:

TC(1)=a(q₁)² and TC(2)=b(q₂)² +2cq₂.

a) Find the first order Conditions and solve for the optimal output levels. Check the SCO (second order Conditions)

b) Solve for (q₁) ^* and find d(q₁) ^*/dc, interpret this the sign of this derivative.