Storable, Renewable Resource: Forest

Storable, Renewable Resource: Forest


(Chapter 12)



Introduction

The forest manager must decide:

1 Whether to harvest a particular stand of trees or2 Wait for the additional growth

The time period between initial investment (planting) andrecovery of that investment (harvesting) is especially long

Intervals of 25 years or more are common in forestry, but notin many other industries.



The Biological Dimension

The Actual growth of a stand of trees depends on manyfactors:Some Ideas....................



The Economics of Forest Harvesting

From the de�nition of e¢ ciency, the optimal time to harvestthis stand would be:

the time that maximizes the present value of the netbene�ts from the wood.

The size of the net bene�ts from the wood depends on:

whether the land will be perpetually committed to forestry orleft to natural process after harvest.

Assume that the land will be perpetually committed toforestry.

There exist two costs which are presumed to be important inthe decision of forest harvesting:

1 Planting Costs2 Harvesting Costs



Example

Example

Planting costs $1, 000Harvesting Costs $0.30 per cubic foot of wood harvested.



The Planning Problem

Our basic model is somewhat unrealistic in several respects



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 lumber is constant andthat the rate of growth of the tree starts high and graduallydeclines.

If there is a competitive market for lumber, When should theforest be cut for timber?

When the growth of the forest is equal to the interest rateBefore that: ?After That: ?



Nash Equilibrium

We can express this more formally by looking at the presentvalue of cutting the forest at time T .

This will be:

We want to �nd the choice of T that maximizes the presentvalue �that is, that makes the value of the forest as large aspossible.



Graphically

Rate of growth offorest

Rate of growth ofMoney

T

Rate of growth ofWealth

Time



Graphically

Invest first in forest, then inbank

Invest only inforest

T

Total Wealth

Time

Invest only inBank



Extending the Basic Model

It considers the harvest as a single event rather than anin�nite sequence of harvesting and replanting.

The single-harvest model we developed would be appropriatefor an in�nite planning period if and only if all periods wereindependent.

Interdependencies do exist

In our single harvest model the optimum age to harvest occurswhen

MB of an additional year�s growth = MgOC of Capital



Extending the Basic Model

The e¤ect of including the opportunity cost of delay in anin�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 forester would harvest at an earlier age when sheis planning to replant the same area than when the plot willbe left inactive.



Problem 1

You are asked to determine the optimal harvest decision (rotationrule) for growing wood on some land. The harvesting cost is $4000per acre. The land value after harvesting is $500 per acre. Themarket price of wood is predicted to stay constant at $20 per cubicfoot. The table below gives the estimated volume of the wood inyour 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 is10%?



Problem 1

a) The rotation time that will give the maximum sustainedyield?

year Cubic feet ofwood/acre

Average yieldper year

1 25 2510 295 29.515 480 3216 520 32.517 561 3318 603 33.519 646 3420 690 34.530 1189 39.6331 1247 40.22532 1306 40.8133 1366 41.3934 1427 41.9735 1488 42.5136 1548 4337 1607 43.4338 1663 43.7639 1716 4440 1766 44.1541 1813 44.2242 1857 44.2143 1897 44.1144 1934 43.9545 1968 43.7350 2094 41.88



Problem 1

b) The rotation time that will maximize pro�ts, if theinterest rate is 5%?

year wood V ∆V (VC+S)*0.05

1 25 500 500 15010 295 5,900 600 12015 480 9,600 740 28016 520 10,400 800 34517 561 11,220 820 38618 603 12,060 840 42819 646 12,980 920 47420 690 13,800 820 51530 1,189 23,780 998 101431 1,247 24,940 1160 107232 1,306 26,120 1180 113133 1,366 27,320 1200 119134 1,427 28,540 1220 125235 1,488 29,760 1220 131336 1,548 30,960 1200 137337 1,607 32,140 1180 143238 1,663 33,260 1120 148839 1,716 34,320 1060 154140 1,766 35,320 1000 159141 1,813 36,260 940 163842 1,857 37,140 880 168243 1,897 37,940 800 172244 1,934 38,680 740 175945 1,968 39,360 680 179350 2,094 41,880 504 1919



Problem 1

c) The rotation time that will maximize pro�ts, if theinterest rate is 10%?

year wood V ∆V (VC+S)*0.1

1 25 500 500 30010 295 5,900 600 24015 480 9,600 740 61016 520 10,400 800 69017 561 11,220 820 77218 603 12,060 840 85619 646 12,980 920 94820 690 13,800 820 103030 1,189 23,780 998 202831 1,247 24,940 1160 214432 1,306 26,120 1180 226233 1,366 27,320 1200 238234 1,427 28,540 1220 250435 1,488 29,760 1220 262636 1,548 30,960 1200 274637 1,607 32,140 1180 286438 1,663 33,260 1120 297639 1,716 34,320 1060 308240 1,766 35,320 1000 318241 1,813 36,260 940 327642 1,857 37,140 880 336443 1,897 37,940 800 344444 1,934 38,680 740 351845 1,968 39,360 680 358650 2,094 41,880 504 3838



Sources of Ine¢ ciency

Perverse Incentives for the Landowner: Forestry provides anunfortunately large number of situations where perverseincentives produce ine¢ cient and unsustainable outcomes.Private forest decisions are plagued by external costs ofvarious types. Harvesting timber imposes costs on othervalued aspects of the forest:

Prevention of soil erosionProtection of biodiversityWatershed maintenance

Failure to recognize all of the social values provides anincentive not only to harvest an ine¢ cient large amount oftimber but also to harvest timber even when the preservationis the e¢ cient alternative.



Sources of Ine¢ ciency

Government policies can also create perverse incentives forlandowners

Example: Brazilian government reduced taxes on incomederived from agriculture (cattle ranching)Overvalued agricultureSubsidized an activity that, in the absence of taxdiscrimination, would not normally have been economicallyviable.Brazilian taxpayers were unknowingly subsidizing deforestationthat depreciated the value of their natural capital stock.



Sustainable Forestry

Rate of deforestation is a¤ected by

the harvesting decisionthe replanting decision andthe conversion decision

Pro�t maximizing decisions may not be e¢ cient (higher ratesof deforestation).

Does the restoration of e¢ ciency guarantee sustainableoutcomes?

Sustainable forestry: would require harvests to be limited tothe growth of the forest, leaving the volume of wooduna¤ected over time.

Choosing the harvest age that max. the PVNB inslow-growing forests may well involve harvest volumes higherthan the net growth of the forest.

The solution: Rapidly growing tree species in plantations.

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Storable, Renewable Resource: Forest