Consider the duopoly computer industry problem with heterogeneous consumers analyzed in Section 2.2.3, but suppose that each computerproducing firm bears a positive production cost. More precisely, assume that each hardware unit costs exactly c > 0 to produce. Answer the following questions.

(a) Calculate the UPE prices and profit level assuming that the brands are incompatible (i.e., how equation (2.23) is modified in the presence of production costs).

(b) Calculate the UPE prices and profit level assuming that the brands are compatible (i.e., how equation (2.25) is modified in the presence of production costs).

(c) Conclude whether Proposition 2.4 on page 31 still holds in the presence of production costs.