PLEASE WORK STEP BY STEP Horizontal Cournot Merger

Consider a homogenous good industry with five identical firms. Inverse demand in this market

is given by

p $=50-1/2$Q:

All n firms have the same constant marginal cost c $=10.$ Suppose firms compete in quantities.

$($a$)$ Calculate the Nash equilibrium in quantities. Give each firm$$s profit.

$($b$)$ Suppose a merger between two firms in this industry decreases the marginal cost of the

merged company to a level of c with $0$ $1.$ Derive the condition under which a two$-$

firm merger is profitable. Briefly discuss this condition.

$.$

$($c$)$ Show that the profit of the non$-$merging firms increases for $=1/2$ and decreases for $=$

$1/4$ due to the merger. Explain the difference.

$($d$)$ The competition authority $($CA$)$ is confronted with the merger proposal of $($b$).$ The

companies claim that the merger will reduce their marginal cost by $50$ percent. Should the

CA allow the merger if their aim is to:

$($i$)$ maximise total welfare

$($ii$)$ maximise consumer surplus

Explain the difference