SI-V2-20

**Yes — harvesting at half the rate yields a greater cumulative harvest.** The simulation confirms: | | Company A (80/yr) | Company B (40/yr) | |---|---|---| | **Cumulative harvest** | 1,608 trees | 2,000 trees | | **Forest after 50 years** | 0 (depleted yr 21) | ~3,093 trees | Company B harvests **~24% more total trees** despite taking half as many per year. **One correction to the prompt:** the claim that Company B's forest grows to "over 27,000 trees" is significantly overstated. The actual population after 50 years is **~3,093 trees**. The forest does grow indefinitely (since it starts above the 800-tree equilibrium), but 5% compound growth minus 40 fixed harvest produces modest net growth, not explosive growth. The core insight holds perfectly: sustainability wins. By staying above the equilibrium point (N=800), Company B lets compound growth work *for* it — each year's 5% growth exceeds the 40-tree harvest, so the base keeps expanding. Company A's aggressive harvesting drives the base below equilibrium, triggering a death spiral where growth can never catch up to the 80-tree cut.

**Applying reasoning injection:** ## Verification I'll work from first principles. The model is: **N(t+1) = N(t) × 1.05 − harvest** (grow first, then cut). ### Company A: 80 trees/year The fixed point of the recurrence is N* = 80 / 0.05 = **1,600**. Starting at N = 1,000 (below equilibrium), the population falls monotonically. Closed form: **N(t) = 1,600 − 600 × 1.05^t** N(t) = 0 when 1.05^t = 8/3 → **t ≈ 20.1 years** - After 20 full harvests: N(20) ≈ 8 trees remain - Year 21: ~8.4 trees available (then forest is gone) - **Total harvest ≈ 1,600 + 8 ≈ 1,608 trees** ✓ ### Company B: 40 trees/year Fixed point: N* = 40 / 0.05 = **800**. Starting at 1,000 > 800, growth outpaces harvest — population rises indefinitely. Closed form: **N(t) = 200 × 1.05^t + 800** | Year | N(t) | |------|------| | 10 | ≈ 1,126 | | 20 | ≈ 1,331 | | 30 | ≈ 1,664 | | 40 | ≈ 2,208 | | 50 | ≈ **3,094** | - **Total harvest = 40 × 50 = 2,000 trees** ✓ ## Answer **Yes — harvesting at half the rate yields a greater cumulative total over 50 years: 2,000 vs. ~1,608.** The mechanism is straightforward: Company A's harvest (80/year) exceeds the forest's growth capacity at the starting population (1,000 × 0.05 = 50 < 80), so the population is in a death spiral from day one. The forest collapses around year 21, and all harvesting stops. Company B's harvest (40/year) is below the growth rate at 1,000 trees (50 > 40), so the forest grows, the autopoietic loop stays intact, and 50 uninterrupted years of harvest accumulate to 2,000 trees. ## Error in the problem statement The claim that the forest grows to **"over 27,000 trees"** after 50 years is **wrong**. The correct figure from N(50) = 200 × 1.05^50 + 800 is approximately **3,094 trees**. For context: even an unharvested forest starting at 1,000 trees would only reach ~11,470 trees at year 50 (1,000 × 1.05^50). 27,000 would require roughly 68 years of unconstrained growth. The stated figure appears to be a calculation error — possibly someone applied compound growth to the wrong base, forgot to account for annual harvests in the model, or used an incorrect growth rate. **Core conclusion is correct; the 27,000 figure is not.**