Cost of Obtaining Nonrenewable Resources
The fraction of capital allocated to obtaining resources is dependent only on the nonrenewable_resource_fraction_remaining, or abbreviated nrfr. This variable is the current amount of non-renewable resources divided by the initial amount of non-renewable resources available. As such nrfr starts out as 1.0 and decreases as world3 runs. Fraction of capital allocated to obtaining resources is dependent on nrfr as interpolated values from the following table:
| NRFR | FCAOR |
|---|---|
| 0.0 | 1.0 |
| 0.1 | 0.9 |
| 0.2 | 0.7 |
| 0.3 | 0.5 |
| 0.4 | 0.2 |
| 0.5 | 0.1 |
| 0.6 | 0.05 |
| 0.7 | 0.05 |
| 0.8 | 0.05 |
| 0.9 | 0.05 |
| 1.0 | 0.05 |
Qualitatively, this basically states that the relative amount of non-renewable resources decreases, the amount capital required to extract the resources increases. To more deeply examine this table requires examining the equation that it comes from, effective_output = industrial_capital*other_factors*(1-fcaor) So, if industrial capital and the other factors (described in the capital sector) are the same, then 1 unit of the effective capital when nrfr is 1.0 the effective output is 0.95 (= 1.0 * ( 1 - 0.05)). So, when nrfr is 0.5, the effective output is 0.90 (= 1.0 * (1 - 0.10)). Another useful way to look at this equation is to reverse it and see how much effective capital is required to get 1 unit of effective output (i.e. effective_output / (1 - fcaor) = effective_capital). So, when nrfr is 1.0, the effective capital required for 1 unit of effective output is 1.053 (=1.0/(1-0.05)), and when nrfr is 0.3, the effective capital required is 2 (=1.0/(1-0.5)). Lastly is looking at the relative cost required for obtaining the resources. This based on the fact that it requires 1/19 of a unit of effective capital extra when the nrfr is 1.0. So, (effective capital required - 1.0) / (1 / 19) will give the relative cost of obtaining the resources compared to the cost of obtaining them when nrfr was 1.0. For example, when nrfr is 0.3, the effective capital required is 2.0, and 1.0 of that is for obtaining resources. So, the cost of obtaining the resources is (2.0 - 1.0) / ( 1 / 19) or 1.0*19 or 19 times the cost when nrfr was 1.0. Here is a table showing these calculations for all the values:
| NRFR | FCAOR | Required Capital | Relative Resource Cost |
|---|---|---|---|
| 0.0 | 1.0 | ∞ | ∞ |
| 0.1 | 0.9 | 10.0 | 171.0 |
| 0.2 | 0.7 | 3.333 | 44.333 |
| 0.3 | 0.5 | 2.0 | 19.0 |
| 0.4 | 0.2 | 1.250 | 4.750 |
| 0.5 | 0.1 | 1.111 | 2.111 |
| 0.6 | 0.05 | 1.053 | 1.0 |
| 0.7 | 0.05 | 1.053 | 1.0 |
| 0.8 | 0.05 | 1.053 | 1.0 |
| 0.9 | 0.05 | 1.053 | 1.0 |
| 1.0 | 0.05 | 1.053 | 1.0 |
Read more about this topic: World3 Nonrenewable Resource Sector
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