Earth is overpopulated, and this story has a grim twist of how some of that might be managed. It is about a poor family that spends the day at an amusement park. Instead of paying money to get in and to go on the various rides, you get an injection each time. Most injections are sterile water, but a small percentage of them are a quick acting poison. You are playing a form of roulette each time you "pay" the admission. The family the story is about is a large one, and the father generously "pays" the admission of his wife and all his children, getting several injections--I remember them waiting in hopeful anticipation for him to survive the entry "fee". A dark, but compelling story.

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    Sounds very similar to "The Tunnel Ahead"; scifi.stackexchange.com/questions/34151/… – Valorum Oct 13 '17 at 17:41
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    Huh - first thin I thought of from the title is Cory Doctorow' "Down and Out in the Magic Kingdom" (I guess that's not necessarily a full-on dystopia). Clearly, not that. – RDFozz Oct 13 '17 at 18:27
  • After reading the linked story from the answer, yes, very dark but compelling. – JohnP Oct 13 '17 at 19:43

"Spending a Day at the Lottery Fair", a short story by Frederik Pohl; first published in The Magazine of Fantasy and Science Fiction, October 1983, available at the Internet Archive.

Of course it wasn't like that for the regular American fairgoers. They had to pay. You could see each family group moving up toward the ticket windows. They would slow down as they got closer and finally stop, huddling together while they decided how to pay, and then one or two of them, or all of them, would move on to the window and reach into the admissions cuff for their tickets. Randolph Baxter had long before made up his mind that there would be no such wrangles on this day for his family. He said simply, "Wait here a minute," and strode up to the window by himself. He put his arm into the cuff, smiled at the ticket attendant and said grandly, "I'll take five, please."

[, , , ,]

"Yes, exactly. Of course, one takes a small chance at every ticket window, and in that sense there is a price for everything. A very carefully computed price, Mrs. Millay, for every hot dog, every show, every ride. To get into the fair in the first place, for instance, costs one decimill — that's 1% of a .0001 probability of receiving a lethal injection from the ticket cuff. Now, that's not much of a risk, is it?" he smiled. "And of course it's absolutely painless, too. As you can see by just looking at the ones who have given their lives inside."

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