The #1 biggest issue here is dependent on how resource-dependent nations utilize the income from resources they gain.
The whole concept Hez refers to is a long-known economic condition called "dutch disease." The problem isn't inherently with natural resources. Rather, the problem occurs when nations come under the false impression that a nonrenewable resource is a stable income.
If a nation's leadership believes its nonrenewable resources are stable incomes, it more often utilizes their budgets as such. Money is used for all forms of government services just like any tax. Economic development isn't seen as necessary under this interpretation as the nation will always have their natural resource (Iran under Ahmadinejad is a pretty good example of this, as he even dipped into the nation's emergency savings fund to pay for social services).
However, it's inherently flawed. As Hez points out, some natural resources (oil is a perfect example) aren't renewable, and thus their economies aren't stable. These nations will inevitably see hard economic times as their single resource dwindles (Once again, refer to Iran. When oil prices hit $60.00 last November, the economy went to hell in a handbasket, it was discovered that there was no reserve savings, and a solid opposition to Ahmadinejad was able to build up in response to his use of oil money).
Rather, natural resource nations should be viewed as temporary blessings. An oil nation can have decades without needing to tax its population. This creates the perfect opportunity for the government to invest in other economic sectors, such as manufacturing, service industries, etc. Economic globalization has allowed most countries to be able to develop the infrastructure for a stable economy even without natural resources, provided they somehow obtain a way to access that infrastructure. Natural resources provide nations with this windfall.
It's surprising... with nearly 0 personal taxes and the huge oil windfall, most of the Middle East should be a flourishing center of industrial growth, as they have the resources to develop the infrastructure and develop the demography enough to become industrialized nations. However, most nations tend to squander their opportunity.
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