Earlier quoted context omitted.
Okay, let's take the monopoly example from wikipedia. Firm prices at monopoly price (60 cents), deadweight loss because all transactions for buyers with marginal benefit between 10 and 60 cents do not occur. Assume some identifiable group of people exists with marginal benefit deadweight loss is smaller. Therefore, price discrimination can reduce deadweight losses.
Close, but your example is missing a crucial piece. Specifically, the marginal cost of producing the product. Let's say the MC is 20 cents at the scale produced (Q1). The second group (students) get a MB of let's say 30 cents. They will not buy at a price of 60 cents, therefore there is a deadweight loss (MC < MB to students, but they do not have the good). If the monopolist can expand their output to Q1 + Q2 (where…
By the way, there's no need to assume MC is a function of Q since that just complicates the example for no benefit (in the wiki article notice that MC is just a constant 10 cents). And yes, though I didn't stress it, of course the discount price must still be greater than the MC (and so in the range of 10 - 60 cents).