1. Production Economics of Renewable and Exhaustible Natural Resources Appendix 7B
Natural resources come in two types
Renewable – such as timber, which can be harvested and replanted
Exhaustible – such as coal and oil, which can run out
Natural resources are often subject to the problem of common property, which can lead to externalities
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2. The Tragedy of the Commons
When there is no ownership of a (common) pond, excessive fishing occurs.
Solutions to excessive fishing include:
Limiting the fishing season or otherwise making fishing more costly or difficult
Limiting effort by taxing it, higher fishing licenses, charging a fee per fish caught
Changing the “common ownership” to creating ownership of the area
Such things as a cooperative
Establishing ownership over the first 200 miles from the coast
Creating quotas that can be transferable. This is the general idea behind Cap and Trade policies

3. A Model of Renewal Resources
S = Capital Asset or Stock – total population or biomass (trees, fish, oysters, etc.)
Change in S over time, DS/Dt = -h + g(S), is negatively impacted by harvesting and positively by the biological growth rate
h = Harvest – how many are extracted (flow), which is a function of E, effort.
E = Effort – how hard fisherman, or loggers try to harvest (economic term)
h = f (S, E), where ∂f/∂E>0 & ∂2f/∂E2 meaning that there is diminishing returns in effort.

4. Optimal Harvesting What is the “best” amount to harvest every year?
Waiting to harvest later increases S, the stock, and then we can sell more later.
Optimal to find where the percentage rate of growth in the value of the timber or fish (P∙DS/Dt)/PS = r, the risk-adjusted discount rate.
Allows us to think of the problem in terms of sustainability

5. 7B.2: Sustainable Yield
hEX
Rate of
Harvest in
lbs/time
h*W/O
Discount
Rate (%) r
Line AD is ROR without (W/O) waiting. Pt. D is optimal
Line through E is ROR with (W/) waiting. Pt E is optimal.
The optimal harvesting is not at MSY.
Harvest is smaller if waiting.
hMSY
h*W/
SW/O
Resource
Capital
Stock
SMSY
S*W/ A D E .
hEX: is nonsustainable harvesting to extinction
hMSY: MSY – max sustainable yield at stock size SMSY
h*W: optimal harvest without waiting.
h*W/O: optimal harvest with waiting.

6. Optimal Extraction & Prices
Waiting only makes sense when the growth rate of the price of the item grows at the discount rate, r, or more.
Hence, PT = P0(1+r)T
With this future price, the current price is the discounted future price: P0= PT∙e-rT
This implies an ever rising price of the extracted resource. P
time

7. Finding the Efficient Harvest
In a fuller model, we would examine human effort (E), changes in technology facility for harvesting, and the size of the
How hard you try is “effort” (E).
Technological facility (f)
Stock size (S)
Harvest could be thought of as a product: h = E*S*f
As the stock is becomes depleted, you need even more effort or greater technological facility to catch the same harvest than you would with a healthy stock.
As oil disappears, we see even greater effort in finding new sources and new ways to extract.