Suppose the two firms merge and regulators want to make sure that welfare is not decreased by the merger. How much would marginal cost have to fall in order for welfare to be identical before and after the merger

Answer: marginal cost = 57

Explanation:

MR = MC

surplus = 20*20/2 = 200

80 - 2Q = MC

Q = 40 - (MC/2)

BUT,

CS = Q * Q/2 = (40 - (MC/2) ²) / 2 = (80-MC) ²/8

also PS = Q * (P - MC)

substituting,

PS = (80-MC) / 2 * (80 - (80-MC) / 2) - MC

simplifying,

PS = (40 - (MC/2)) * (40 - (MC/2))

PS=1600-40MC+MC²/2

since we now have the value of PS and CS,

thus related by,

CS+PS=200

(6400 - 160MC + MC²) / 8 + (1600 - 40MC + MC²/4) = 200

2400 - 60MC + 3MC²/8 = 200

solving quadratically,

MC = 56.9 ~ 57

MC = 57