oligopoly

[anon_econ]

A lemon growing cartel consists of four orchards. Their total cost functions are:
TC1=20+5(Q1)^2
TC2=25+3(Q2)^2
TC3=15+4(Q4)^2
TC4=20+6(Q4)^2

a) If the cartel decided to ship 10 cartons per month and set a price of 25$ per carton, how should output be allocated among firms?
b) At this shipping level, which firm has the maximum incentive to cheat? Does any firm not have an incentive to cheat?

for the first part i equated the MCs to get the allocation and got the output for each firm. but i can't figure out the second part..i tried to find the profit maximizing level of output for each firm given that the price is 25$ and compare it to the output found in part 1 but it's not working out..plz help!

[komal]

I think everyone would like to cheat because their mc has not yet reached to 25, so producing more and selling it for p slightly less than 25 would be profitable to all.
when u would be comparing the output of firms with and without cartel , u will find that the maximum diff in output and profit will be for the second firm, so basically second firm has most incentive to break cartel

[anon_econ]

Yea ok i was doing the same thing but somehow i thought there was something wrong :/
Thanks :)