The World State's response to overpopulation is to regulate the type and number of the population on a global scale.
According to Aldous Huxley's Brave New World, the World State is the entity responsible for keeping the population at an optimum number for each succeeding generation. By its calculation, a population of under two billion is the ideal population number to support global welfare. To ensure the realization of its population goals, the World State relies on eugenics and dysgenics.
Eugenics basically refers to the breeding of superior human beings for the welfare of global societies. Conversely, in Brave New World, dysgenics refers to the breeding of inferior human beings for the purposes of supporting the higher-skilled populations of the earth.
In his novel, Huxley introduces the idea the population of the earth must not only be maintained at a certain number, but also that the number of that optimum population must be carefully apportioned among the genetically superior and the genetically inferior. This ensures the majority of the population is composed of genetically superior humans.
In the novel, biologically superior ova and sperm are fertilized and decanted as superior species of Alphas, Betas, and Alpha Pluses. To ensure a class of almost sub-human beings are able to support the genetically superior beings, inferior ova is combined with inferior sperm to produce Gammas, Deltas, and Epsilons. As an additional step, the Gammas, Deltas, and Epsilons are exposed to what is called Bokanovsky's Process. The novel describes the process:
One egg, one embryo, one adult-normality. But a bokanovskified egg will bud, will proliferate, will divide. From eight to ninety-six buds, and every bud will grow into a perfectly formed embryo, and every embryo into a full-sized adult. Making ninety-six human beings grow where only one grew before. Progress.
In the novel, Bokanovsky's Process is combined with Podsnap's Technique, which speeds up the maturation of unfertilized eggs to produce a vast number of these genetically inferior beings. The Gammas, Deltas, and Epsilons are used to perform unskilled, menial labor; the World State keeps this group content in its servile condition by providing the members of this subhuman group easy and plentiful access to gratuitous entertainment, sexual fulfillment, and daily doses of soma (a pleasure drug). Since drugs like cocaine and heroin aren't legally available in the dystopian world of the novel, soma is the only available means by which the World State can protect itself from rebellion within its borders; it's an insurance policy against uprisings and societal unrest.
To prevent over-producing humans of either genetically superior or inferior stock, the World State only allows 30% of female embryos to develop normally. The others develop into what are called freemartins: sterile women developed from female embryos that were periodically injected with male sex hormones.
Since the World State makes all decisions for citizens, they also decide when human beings die. Those who are too sick and old are not allowed to burden society with their infirmities. Death conditioning begins at the age of eighteen months; every toddler spends at least two mornings a week at the Hospital for the Dying.
So, to recap, the World State's response to overpopulation is to control the number and type of citizenry as well as to utilize euthanasia to dispose of what the state considers useless citizens.