What is humanity's real problem — climate change or peak oil?

Answer: neither — they just aspects of a bigger problem that includes our still-expanding population.

World population passed 7 billion late in 2011 or early in 2012¹. Around one third of those 7 billion live in varying degrees of wealth, with more than enough food. Indeed, the dietary habits of the wealthy third are characterised by growing incidence of obesity & overweight. This is the same third that is largely responsible for climate change, & will be most affected by peak oil.

Of the remaining two thirds, many have a reasonable standard of living & enough to eat. Some though, live in poverty with malnutrition & famine a constant threat. You've seen the photos.

World population is expected to pass 9 billion around 2050¹. I.e. two billion more than we can't feed now.

http://www.resilience.org/stories/2014-09-02/why-peak-oil-refuses-to-die
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¹ World population
http://en.wikipedia.org/wiki/World_population / fears imminent peak decline world oil production environmental problem oil supplies planet Earth petroleum resources peak-oil debunk extracting extract extraction resources affordable oil industry costs of production very high oil prices resources tight oil Arctic oil ultra-deepwater oil bitumen deep water US economy recession $20 per barrel oil $100 per barrel oil industrialized countries response oil producers liquid hydrocarbons industry apologists environmentalists global warming climate change carbon dioxide monoxide CO2 greenhouse effect fossil fuel energy transition substitution efficiency low-carbon energy sources solar wind nuclear use energy smarter electrify transport battery powered cars electric vehicle EV battery LiIon lithium ion anthropogenic climate change environmental issue humanity humanity transition to renewable energy politics regulation climate campaigners electricity sector variability wind solar power energy storage capacity redundancy grid upgrades /