Assume that a monopolist is concerned that another firm will enter its market. It is considering a brand proliferation strategy to deter entry. If the monopolist invests in a brand proliferation strategy, this raises its cost and the cost of the potential entrant by $>0.$ Firms play a two$-$stage game. In the first stage, the monopolist $(M)$ decides to invest in brand proliferation or not. In the second stage, the potential entrant $($PE$)$ decides to enter or not. Payoffs $()$ are as follows:

i$.$ With no brand proliferation and no entry, ${}_M=36$ and ${}_{PE}=0.$

ii$.$ With no brand proliferation and entry, ${}_M=20$ and ${}_{PE}=12.$

iii. With brand proliferation and no entry, ${}_M=36-$ and ${}_{PE}=0.$

iv$.$ With brand proliferation and entry, ${}_M=20-$ and ${}_{PE}=12-.$

A$.$ Describe this game in extensive form.

B$.$ Identify the value of $$ that will keep PE from entering the market.

C$.$ Identify the value of $$ that will make brand proliferation a profitable strategy for $M.$

D$.$ Is this form of brand proliferation socially desirable? Explain.

Assume that a monopolist produces two software programs, one to solve math problems $(M)$ and the other to solve statistics problems $($S$).$ There are only three consumers $($A$,$ B$,$ and C$)$ who are interested in them. Their preferences are as follows:

i$.$ Consumer A values M at $$50$ and S at $$30.$

ii$.$ Consumer B values M at $$80$ and S at $$40.$

iii. Consumer C values M at $$100$ and S at $$50.$