Monopolist Problem

5. A monopolist produces two different goods. The (inverse) demand for
each good is given as:

p1 =  - q1 + q2

p2 =  + q1 - q2

The monopolist produces both of these goods at a constant unit cost (c >
0) and maximizes the profit function below by setting the output of each
good.

 = p1q1 + p2q2 - cq1 - cq2

You can interpret the parameters as follows. The parameter is the
intercept term for both demand functions. Note that it is necessary for
 > c. The  and  parameters are measures of differentiation.
As  gets smaller, or as  gets larger, the products are
increasingly heterogeneous.

Find the equilibrium levels of output for goods 1 and 2.

Show whether these levels of output maximize profits.

c. Use comparative statics to show whether this monopolist’s
equilibrium profits will rise or fall if the monopolist makes these
goods more similar (i.e. more homogeneous). That is, as  and 
change.