dse 2008 Q14 doubt

[bhavya jain]

A monopoly faces the demand curve P = 8 – Q. The monopoly has a constant unit
cost equal to 5 for Q ≤ 2 and a constant unit cost equal to 3 for Q > 2. Its profit
maximizing output equals:
a) 3/2
b) 2
c) 5/2
d) Both 3/2 and 5/2
why the ans to this be d). Actually it shud be c) with the reasoning as follows-
a) profit(with q=3/2)=2.25
b) profit(with q=2)=2
c) profit (with q=5/2)=6.25
clearly profit with 5/2 is the greatest among all, so it's profit max output should be 5/2 only..

[mrittik]

MR=MC, 8-2Q=5=>Q=3/2<2, 8-2Q=3=>Q=5/2.....understood?

[bhavya jain]

yes this is true. but Mrittik don't u think we are asked here about profit max output & clearly profit is greater in case of 5/2, then 3/2. so the monopolist shud produce 5/2 only..ur views..

[mrittik]

it depends upon the quantity itself.....1st the Quantity less than 2.....2nd one is greater than 2....thats why for both cases it is profit maximizing output....