1. Dynamic Efficiency

So far we have learned that resource allocation is socially efficient in the instances when it is not possible to increase the net benefit to society by any reallocation. However, we were analyzing static efficiency since our simple model was based on a balance between two current year quantities.

Future Time Periods

Now we are ready to include several future time periods into our analysis to study dynamic (inter-temporal) efficiency. This is important since time and capital are essentially the largest inputs within forestry. In other words, forestry is a capital-intensive activity with very long production periods (rotations). This capital-intensity is fundamentally reflected in the profitability analysis of forestry investments and in the evaluation of forest properties (forest appraisal). As an example, according to Niskanen et al. (2002) the profitability of forestry may seem exceptionally good when compared to any other activity, especially if we simply sum up the revenues and costs of forestry without taking into account the temporal differences between revenues and costs.

Dynamic efficiency can be defined as resource allocation over time - where it is not possible to increase welfare by any reallocation. Now we are comparing the use of investment calculations the time series of benefits and costs (including also future consequences from today's decisions), not just current period ones. The temporal differences are taken into account by translating these future values into a single metric by converting them into present values (i.e., discounting them). By discounting we make benefits and costs at various time points commensurable. With dynamic efficiency - we mean a choice of resource allocation (time series) that gives the highest net present value. We will see that the discount rate plays a critical role in dynamic efficiency.

Next, let us illustrate these fundamental concepts. We can simplify the analysis by assuming no taxes, no inflation, no risk and no un-costed environmental benefits from forestry. At first, with an investment, we can acquire or produce a durable good (asset) for which we can expect to receive revenue or other utilities over time. Actually, we can expect to receive more than was paid for the investment. The reason for this is that by investing we give up the opportunity to consume that money now. This extra requirement is called "interest" or "rate of return".

We can also borrow money from capital markets to be paid back from our future earnings. In this case we also have to pay more than was initially borrowed for investment. We can invest (or save) some fraction of what our current period income on financial assets, (i.e., savings accounts to be consumed in the future) but with interest earned. Overall, the discount rate links forest management to capital markets (i.e., other investment opportunities). On the other hand, well-functioning capital markets are necessary conditions for dynamic efficiency. This is one example of a general principle in economics: different markets are interconnected, thus everything affects everything else.

By investing in forestry, we give up an opportunity for earnings elsewhere on that capital. Thus the interest rate is the cost of an opportunity forgone, an opportunity cost of capital. Primarily, the interest rate controls the amount of capital bound in forestry (mainly the volume of the growing stock). If, for example, the minimum acceptable rate of return in forestry is not realized, the rational forest owner has to sell his forest or reduce the amount of capital bound on forestry (i.e., with thinnings or final cuttings).

Let us assume that a forest owner can earn 10 % interest annually on his savings from harvest revenue. Below you can see the values of savings over time:

 Time Value of savings: Increment 0 1 =1 1 1(1+0.1) =1(1+0.1)=1.10 0.10 2 1(1+0.1)(1+0.1) = 1(1+0.1)2 = 1.21 0.11 3 1(1+0.1)(1+0.1)(1+0.1) = 1(1+0.1)3 = 1.33 0.12 4 1(1+0.1)(1+0.1)(1+0.1)(1+0.1) = 1(1+0.1)4 = 1.46 0.13

The increment is increasing because the interest is earned not only on the original capital, but also on the accumulated interest. This is the essence of compounding (accumulation) and compound interest. In general, we can write the formula for compounding as:

where r=interest rate, V0=initial value (investment), Vn=future value at time n. Compounding results in a future value Vn at time n from initial value (investment) V0 at interest rate r. An example is given in Figure E7.

The present value of any single future value can be found by solving a compounding equation as follows:

An example is given in Figure E8. We can solve the compounding equation also for r, which is the average annual rate of return, the internal rate of return on an investment for which you paid V0 and received Vn n several years later.

Figure E7: Compounding: Future value for 1000 euros cutting revenue saved for 30 years at 3 %, 5 % and 7 % interest rates

Figure E8: Discounting: Present value of 1000 euros future cutting revenue (in year 30) at 3 %, 5 % and 7 % interest rates