STOCKHOLM — Angus Deaton of Princeton University won the Nobel prize in economics Monday for improving understanding of poverty and how people in poor countries respond to changes in economic policy. Deaton, 69, won the $975,000 prize from the Royal Swedish Academy of Sciences for work that the award committee said has had “immense importance for human welfare, not least in poor countries.” Committee member Jakob Svensson said Deaton introduced the “Almost Ideal Demand System,” now a standard tool governments use to study how a change in economic policy — say, an increase in sales taxes on food — will affect different social groups and how large the gains or losses will be.