Plesse for a working on paper with pen $....$Horizontal Merger with Price Competition

Consider a homogenous good industry with three firms i $\{1,2,3\}.$Total demand is given by

D$($p$)=230-$p:

The variable $(=$marginal$)$cost of each of the firms is c$1=30,$c$2=40$and c$3=50.$Firms

compete in prices.

$($a$)$Give the Nash equilibrium in prices and all firms$$equilibrium profits. Calculate consumer

surplus.

$($b$)$Suppose firms $1$and $2$are intending to merge. The marginal cost structure of the

potentially new entity is $=20.$Give the new Nash equilibrium in prices and all firms$$

profits if the merger goes ahead. Calculate consumer surplus.

$($c$)$Is the merger profitable for the two firms? Mark the equilibrium allocations of a$)$and b$)$on

the demand curve in a p$,$q diagram. Show total welfare in a$)$and b$)$in your diagram and

mark the social cost and benefit of the merger. Explain the social cost and benefit briefly.

Calculate the social cost and benefit of the merger. Should the merger be approved or

declined?