-suppose prices are announced simultaneously, what are the equilibrium prices Pa,Pb, and Ps?

Question

Consider the pricing problem between two independent firms, Firm A and Firm B that make complement products..?

Call these products A and B and denote their prices Pa+Pb respectively. Products A and B have zero marginal cost and are used to make an integrated system S. The demand for this system is given by equation Qs(Ps)=180-1/3Ps, where Ps=Pa+Pb....

-suppose prices are announced simultaneously, what are the equilibrium prices Pa,Pb, and Ps?

-Suppose Firm A announces its price first,what are the equilibrium prices Pa,Pb,and Ps?

-Suppose Firm A and B merge into one company..what is the equilibrium price,Ps?

-where are prices the lowest? why is this unusual?

Answer 1

I know Macroeconomics better.

The only solution I see is for "-Suppose Firm A and B merge into one company..what is the equilibrium price,Ps?" question.

If they are mergers then they act as single monopolist, and MC=0, so Profit(max) then MR->MC or MR->0

MR=(TR)'

TR=Q*P

TR=180P-(P^2)/3

MR=(180P-(P^2)/3)' = 180-2P/3

180-2P/3=0

180=2P/3

P=180*3/2=90*3=270

Answ: P=270