4.1. Timber supply function
It is well known that a nonlinear optimization problem may have multiple local optimal solutions. In an attempt to find the global optimal solution, we solved the optimization problem repeatedly using different starting points, both for the benchmark case and the case when IRMs are used in forest regeneration. Table 3 presents 10 optimal solutions in the benchmark case (when IRMs are not available), in the order of a decreasing objective function value. These solutions were obtained using the same set of timber demand scenarios, and hence the objective function values associated with different solutions are directly comparable. To be more certain about the relative performances of the different supply functions, we estimated the EPV of the total surplus associated with each of the supply functions in Table 3 using additional 10 different sets of timber demand scenarios, where each set consists of 1000 scenarios. The results for the first two supply functions are presented in Table 4. The last column in Table 4 shows the difference in the EPV of the total surplus between the first and the second solution presented in Table 3. The results in Table 4 show clearly that the first solution is superior to the second one.7 The simulations showed that the first solution led to significantly larger EPV than each of the other nine solutions. Therefore, we chose the first solution in Table 3 as the global optimum for the benchmark case. That is, the optimal market supply function in the absence of IRMs is
Table 3. Optimal values of the supply function coefficients and the expected present value of the total surplus (billion SEK) in the absence of regeneration materials.
|Solution no.||α1||α2||α3|| E[TSb(αb)]|
Table 4. Estimates of the expected present values of total surplus (billion SEK) associated with the first two solutions presented in Table 4. Each estimate is the average of 1000 random samples.
|Simulation no.||Solution no. 1||Solution no. 2||Difference|
Following the same procedure, we obtained the optimal supply function in the presence of IRMs
What may appear remarkable about the supply functions is that the inventory elasticity and the price elasticity are abnormally high. It should be emphasized that most of the solutions we obtained do have “normal” inventory and price elasticity (see Table 3 for the benchmark case). Yet, these solutions lead to a lower EPV of the total surplus, which implies that these supply functions do not provide better descriptions of the relationship between timber supply and the explanatory variables.
The inventory elasticity of timber supply depends partly on the definition of inventory and the assumption about the area of forestland. For example, a change in the mature timber stock would have a larger impact on supply than a change in the total timber inventory in the forest. One can also imagine that the effect of increasing timber stock caused by an increase in the share of older stands in a forest would be larger than when the timber stock increase is caused by an expansion of the forest area. Likewise, the price elasticity of timber supply may depend on the age-class distribution of the forests. In this study, we used the mature timber stock (timber inventory in stands which are older than 60 years) as an independent variable in the supply function. The total area of forestland was fixed, which, together with the ranking rule used to select the stands to harvest, imply that the mature timber stock changes only through the change in the area of the oldest stands in the forests. The initial mature timber stock is over 2000 million m3, which is about 20 times larger than the annual harvest volume. With this background, it is not surprising that the inventory elasticity of supply is very high. The existence of this enormous mature timber stock is also the reason why the price elasticity of timber supply is high. When there is a large amount of timber in old stands, a small increase in timber price would cause a considerable change in the harvest volume.
4.2. Welfare effects
To obtain reliable estimates of the welfare effects of using IRMs, we re-estimated the EPV of the total surplus through an extended simulation based on 1000 demand scenarios in each of the three cases: the benchmark case, the case with the new forest growth function and the benchmark supply function, and the case with the new growth function and new supply function. For each the three cases, 20 replications of the extended simulation were conducted.
Table 5 presents the EPVs of producer surplus (forest management profits), consumer surplus, and the total surplus in the benchmark case. The huge EPVs of consumer surplus and total surplus are mainly the results of the iso-elastic demand function. One should keep in mind that it is the changes in the consumer surplus and in the total surplus that are important. The absolute values of the consumer surplus and the total surplus are not directly relevant.
Table 5. The expected present values of producer surplus, consumer surplus, and total surplus in the absence of IRMs (unit: billion SEK).
|Simulation no.||Producer surplus||Consumer surplus||Total surplus|
The EPV of forest management profits also appears to be very large. The actual profit from timber production in Sweden during 1987–2006 was, on average, 11.85 billion SEK per year (see Table 6). If we assume that the profit will remain at this level in the future, then with an interest rate of 3% the present value of all future profits would be 395 billion SEK, which is about 60% of the EPV shown in Table 5. In our analysis, we included timber harvest and regeneration costs, but ignored the costs of all other management activities such as forest road construction and maintenance, drainage, and precommercial thinning. The total cost of these activities is about 1.5 billion SEK per year. The present value of these costs is in the order of 50 billion SEK. Another simplification, which leads to overestimation of the EPV of future profits, is that we ignore thinning in our analysis. A considerable portion of the existing forests has been thinned before, and the growing stock of timber in the existing forests is lower than the estimate produced using the yield function (13). Compared with the data from national forest inventory (Swedish Forest Agency ), the yield function (13) overestimates the initial mature timber stock in the existing forests by about 800 million m3. Very roughly, this means an overestimate of forest owners’ profits of 100 billion SEK. After these two biases are corrected, our estimate of the EPV of forest owners’ profits reduces to 476 billion SEK, which is 20% higher than the value estimated based on the actual profits.
Table 6. Annual revenues, costs, and profits of timber production in Sweden during 1987–2006 (billion SEK at 2006 price level). Source: Statistical Yearbook of Forestry.
When determining the aggregate timber supply function, we assumed that the timber market is perfectly competitive and ignored the impact of timber harvest on the non-timber benefits of the forests. Most forest owners in Sweden have multiple objectives and do not maximize solely the profits from timber production (Carlen , Andersson and Gong ). Moreover, the timber market in Sweden is not fully competitive on the demand side, which further reduces the profits of timber production (Brännlund et al. , Brännlund ). The EPV of the forest owners’ profits associated with the optimal supply function ought to be higher than the actual profits. There is no precise estimate of the potential increase in the timber production profits in Sweden that can be used to verify our results. However, it is not unrealistic that the present value of future profits can increase by 20% if the timber market is perfectly competitive, and the forest owners manage their forests to maximize the profits from timber production.
The biases should not have any significant impact on the estimated effect of IRMs on the EPV of forest owners’ profits, as the other management costs and thinning were ignored in both the absence and presence of IRMs.
Table 7 presents the EPV of the total surplus associated with different supply functions, in the presence of IRMs. Column C1 gives the estimates of the EPV of the total surplus when IRMs are used but the forest owners do not change their harvest behavior. The figures in Column C2 are the differences between the EPV estimates in column C1 and the corresponding estimates in the benchmark case (shown in the last column of Table 5), that is, the direct effect on welfare of IRMs. Column C3 presents the estimates of the EPV of the total surplus when IRMs are used and the forest owners change their harvest behavior accordingly. The resulting changes in the EPV of the total surplus (column C4) are, therefore, estimates of the total welfare effect of IRMs. The last column of Table 7 shows the effect of changing harvest behavior.
Table 7. The expected present values of the total surplus in the presence of IRMs, estimated using different supply functions (unit: billion SEK).
|Simulation no.||Benchmark supply function||Optimal supply function||Effect of changing harvest behavior C4-C2|
|ETS C1||Change C2||ETS C3||Change C4|
From Table 7, we see that the direct effect of using IRMs on the EPV of the total surplus is 27.41 billion SEK, and the total effect is 33.61 billion SEK. Accordingly, the effect of changing harvest behavior is 6.2 billion SEK, or about 18% of the total effect.
Table 8 summarizes the effects of IRMs on the EPVs of forest owners’ profits and consumer surplus. The results show that access to IRMs causes the profits of timber production to decrease and the consumer surplus to increase. Once IRMs become available, they will be applied on large scales. This is simply the result of the force of competitive markets. As long as no single forest owner can influence the price of timber, it is better for the forest owner to use IRMs irrespective of whether the other forest owners use them or not. Widespread application of IRMs would cause timber supply to increase and timber price to decrease. If the price elasticity of timber demand is sufficiently large, the price effect would outweigh the effect of increasing the harvest on the forest owners’ profits.
Table 8. The expected present values of producer surplus and consumer surplus in the presence of IRMs (unit: billion SEK).
| ||Producer surplus||Changea||Consumer surplus||Changea|
|Benchmark supply function||596.72||−30.10||21,908.75||57.50|
|Optimal supply function||583.35||−43.45||21,928.31||77.06|
In a competitive market, forest owners behave as price takers. From the point of view of an individual forest owner, using the IRM would increase future timber yield but would not affect the evolvement of timber prices. In other words, for each forest owner, the access to IRMs implies that the value of forest land and, hence the opportunity cost of keeping the existing stands growing, increases. Therefore, the presence of IRMs would cause a forest owner to harvest the existing stands at lower ages. Simulations using the benchmark supply function do not capture this response by the forest owners, and therefore do not provide us with an estimate of the full welfare effect of IRMs.
Figure 4 presents the expected annual supply of timber both in the absence and in the presence of IRMs, over a time period of 200 years. Figure 5 presents the expected timber prices corresponding to the time paths of supply presented in Figure 4. These two figures are helpful in understanding the difference between the direct effect and the total effect of using IRMs on the EPV of the total surplus. When simulated using the benchmark supply function, the presence of IRMs has no effect on the expected timber supply and the price during the first 60 years, and causes the timber supply to increase and the price to decrease thereafter. The reason is that, without considering the change in harvest behavior, IRMs would affect the supply and the price only through the impact on the mature timber stock. The mature timber stock is not affected by the use of IRMs before the first stands regenerated using the IRMs have reached a mature age. Simulation results using the optimal supply function, in which the change in the harvest behavior is embedded, show that the timber supply would increase and the price decrease immediately after IRMs become available. As a result, the mature timber stock in the initially existing forests is depleted at a faster rate in the presence of IRMs, which has a negative effect on future supply. As time passes, the effect on timber supply of the decrease in the mature timber stock becomes greater and would eventually outweigh the positive effect of the change in harvest behavior. When the stands regenerated using the IRMs have reached a mature age, the mature timber stock starts to increase and so does the aggregate supply of timber.