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 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1

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

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.

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

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.

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

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.