Posted this in /biz/ as well but I feel I may have more luck here. I'm betting at least some of you have done economics. So here's my dilemma, /sci/:

This is just a snippet of a problem I had to do for Intermediate Micro. It's a quantity discount problem where the firm is trying to create a plan such that people with the pic related demand curve choose to buy less as a higher price, while for another demand curve people choose to buy more at the discount rate (for the other curve, MR=MC results in Q=300 and P=0.10, hence why this was the plan chosen). What doesn't make sense to me is that, for this plan with this particular curve, not only do the consumers choose to go with the plan that was not made for them, but profits increase under this plan. So it's an incentive incompatible plan, but profits are higher.

I've been trying to figure out where I've made a mistake but I cannot find one. What gives?

(I know profits might be hard to see, but under the higher price it's $12 and under the lower one it's $15).

You can check the math- for MR = MC, the profit maximizing quantity should be 120.