Storable, Renewable :

Storable, : Forest

(Chapter 12) Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Introduction

The forest manager must decide:

1 Whether to harvest a particular stand of or 2 Wait for the additional growth

The time period between initial investment (planting) and recovery of that investment (harvesting) is especially long Intervals of 25 years or more are common in , but not in many other industries. Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest The Biological Dimension

The Actual growth of a stand of trees depends on many factors: Some Ideas...... Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest The Economics of Forest Harvesting

From the de…nition of e¢ ciency, the optimal time to harvest this stand would be: the time that maximizes the present value of the net bene…ts from the . The size of the net bene…ts from the wood depends on: whether the will be perpetually committed to forestry or left to natural process after harvest. Assume that the land will be perpetually committed to forestry. There exist two costs which are presumed to be important in the decision of forest harvesting:

1 Planting Costs 2 Harvesting Costs Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Example Example

Planting costs $1, 000 Harvesting Costs $0.30 per cubic foot of wood harvested. Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest The Planning Problem

Our basic model is somewhat unrealistic in several respects Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest When to cut a forest?

Suppose that the size of a forest is some function of time, F (T ). Suppose further that the price of each is constant and that the rate of growth of the starts high and gradually declines. If there is a competitive market for lumber, When should the forest be cut for timber? When the growth of the forest is equal to the interest rate Before that: ? After That: ? Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Nash Equilibrium

We can express this more formally by looking at the present value of cutting the forest at time T . This will be:

We want to …nd the choice of T that maximizes the present value –that is, that makes the value of the forest as large as possible. Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Graphically

Rate of growth of Rate of growth of Wealth forest

Rate of growth of Money

Time T Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Graphically

Total Wealth Invest first in forest, then in bank

Invest only in forest

Invest only in Bank

Time T Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Extending the Basic Model

It considers the harvest as a single event rather than an in…nite sequence of harvesting and replanting. The single-harvest model we developed would be appropriate for an in…nite planning period if and only if all periods were independent. Interdependencies do exist In our single harvest model the optimum age to harvest occurs when

MB of an additional year’sgrowth = MgOC of Capital Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Extending the Basic Model

The e¤ect of including the opportunity cost of delay in an in…nite horizon model is important! Assuming that all other aspect of the problem are the same

The optimal rotation is shorter in the in…nite-planning case than in the single-harvest planning case

Existence of the Opportunity Cost of Delaying the next harvest The e¢ cient would harvest at an earlier age when she is planning to replant the same area than when the plot will be left inactive. Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Problem 1

You are asked to determine the optimal harvest decision (rotation rule) for growing wood on some land. The harvesting cost is $4000 per acre. The land value after harvesting is $500 per acre. The market price of wood is predicted to stay constant at $20 per cubic foot. The table below gives the estimated volume of the wood in your forest in various years if you let it continue to grow. What is a) The rotation time that will give the maximum sustained yield? b) The rotation time that will maximize pro…ts, if the interest rate is 5%? c) The rotation time that will maximize pro…ts, if the interest rate is 10%? Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Problem 1

a) The rotation time that will give the maximum sustained yield?

Cubic feet of Average yield year wood/acre per year 1 25 25 10 295 29.5 15 480 32 16 520 32.5 17 561 33 18 603 33.5 19 646 34 20 690 34.5 30 1189 39.63 31 1247 40.225 32 1306 40.81 33 1366 41.39 34 1427 41.97 35 1488 42.51 36 1548 43 37 1607 43.43 38 1663 43.76 39 1716 44 40 1766 44.15 41 1813 44.22 42 1857 44.21 43 1897 44.11 44 1934 43.95 45 1968 43.73 50 2094 41.88 Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Problem 1

b) The rotation time that will maximize pro…ts, if the interest rate is 5%?

year wood V DV (V•C+S)*0.05 1 25 500 500 •150 10 295 5,900 600 120 15 480 9,600 740 280 16 520 10,400 800 345 17 561 11,220 820 386 18 603 12,060 840 428 19 646 12,980 920 474 20 690 13,800 820 515 30 1,189 23,780 998 1014 31 1,247 24,940 1160 1072 32 1,306 26,120 1180 1131 33 1,366 27,320 1200 1191 34 1,427 28,540 1220 1252 35 1,488 29,760 1220 1313 36 1,548 30,960 1200 1373 37 1,607 32,140 1180 1432 38 1,663 33,260 1120 1488 39 1,716 34,320 1060 1541 40 1,766 35,320 1000 1591 41 1,813 36,260 940 1638 42 1,857 37,140 880 1682 43 1,897 37,940 800 1722 44 1,934 38,680 740 1759 45 1,968 39,360 680 1793 50 2,094 41,880 504 1919 Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Problem 1

c) The rotation time that will maximize pro…ts, if the interest rate is 10%?

year wood V DV (V•C+S)*0.1

1 25 500 500 •300 10 295 5,900 600 240 15 480 9,600 740 610 16 520 10,400 800 690 17 561 11,220 820 772 18 603 12,060 840 856 19 646 12,980 920 948 20 690 13,800 820 1030 30 1,189 23,780 998 2028 31 1,247 24,940 1160 2144 32 1,306 26,120 1180 2262 33 1,366 27,320 1200 2382 34 1,427 28,540 1220 2504 35 1,488 29,760 1220 2626 36 1,548 30,960 1200 2746 37 1,607 32,140 1180 2864 38 1,663 33,260 1120 2976 39 1,716 34,320 1060 3082 40 1,766 35,320 1000 3182 41 1,813 36,260 940 3276 42 1,857 37,140 880 3364 43 1,897 37,940 800 3444 44 1,934 38,680 740 3518 45 1,968 39,360 680 3586 50 2,094 41,880 504 3838 Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Sources of Ine¢ ciency

Perverse Incentives for the Landowner: Forestry provides an unfortunately large number of situations where perverse incentives produce ine¢ cient and unsustainable outcomes. decisions are plagued by external costs of various types. Harvesting timber imposes costs on other valued aspects of the forest: Prevention of Protection of Watershed maintenance Failure to recognize all of the social values provides an incentive not only to harvest an ine¢ cient large amount of timber but also to harvest timber even when the preservation is the e¢ cient alternative. Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Sources of Ine¢ ciency

Government policies can also create perverse incentives for landowners Example: Brazilian government reduced taxes on income derived from (cattle ranching) Overvalued agriculture Subsidized an activity that, in the absence of tax discrimination, would not normally have been economically viable. Brazilian taxpayers were unknowingly subsidizing that depreciated the value of their stock. Storable, Renewable Resource: Forest Storable, Renewable Resource: Forest Sustainable Forestry

Rate of deforestation is a¤ected by the harvesting decision the replanting decision and the conversion decision Pro…t maximizing decisions may not be e¢ cient (higher rates of deforestation). Does the restoration of e¢ ciency guarantee sustainable outcomes? Sustainable forestry: would require harvests to be limited to the growth of the forest, leaving the volume of wood una¤ected over time. Choosing the harvest age that max. the PVNB in slow-growing may well involve harvest volumes higher than the net growth of the forest. The solution: Rapidly growing tree species in .