1. Stumpage and Timber Demand


Before reading this section, please review the "demand curve" in ECON1 and consumer preferences in FOR8.

Now we are ready to analyze timber markets and timber price determination. Earlier we introduced stumpage value as S(T)=pf(T), where p was unit stumpage price. Now we can see how the stumpage price - and consequently cutting revenues- are actually determined.

The stumpage price (€/m3) is the unit value that buyers pay for standing timber (here we again ignore the non-timber benefits for simplicity). From the buyer's point of view the stumpage price represents a residual value that remains after subtracting the manufacturing costs and the costs of logging and hauling (all from the sale price of the end product). Therefore, higher sale prices for end products lead to higher stumpage prices and higher logging costs (i.e., because of difficult terrain) respectively to lower stumpage prices.

We have already studied the markets for seedlings and found that the market price in general is affected both by supply and demand factors. Thus, the residual value corresponds to the actual market price only by chance. With the exception of fuel wood, timber is not usually directly used for consumption. Instead it requires further processing for final wood products like paper, plywood, sawn goods and so on. So in other words, wood-products and pulp and paper industries use timber together with other inputs to produce final products for consumers.

The consumers of final wood products can be located very far away from stumpage. International trade is an important factor in balancing the possible gap between the domestic supply of and demand for wood and wood products. It is also important to note that in order to satisfy consumers' needs for final products, it is possible to transport 'timber' in several forms (i.e., as (raw) timber, as pulp (intermediary product) or as paper (final product). In the near future the highest growth demand for paper products is predicted for China, other Asian countries and Latin America.

Derived demand for timber

In ECON1 we derived the demand curve from the principle of diminishing marginal utility. Seedlings, however, are not consumed directly by forest owners. Instead forest owners use seedlings as inputs to produce different timber assortments (i.e., logs, pulpwood and fuel wood). Therefore, similarly as in the case of timber, we are dealing with derived demand which stems first from (possibly foreign) consumers' demand for final wood products and secondly from the significance (role) of timber (seedlings) input in the production process.

The demand for wood end products determines the location of the demand curve for timber. So changes in the end product demand also imply shifts in timber demand (other things being equal). Figure E14 illustrates such a shift in demand for timber as a result of an increase in the end product demand caused (i.e., income rise, population growth or changed consumer preferences (see also FOR8). As a result of this shift, the market price for timber increases from P0 to P1 and cuttings increased from Q0 to Q1. These changes also imply an increase in gross stumpage earnings to forest owners (from P0Q0 to P1Q1). The consumer demand for wood end products is the driving force that creates the demand for timber and has a crucial impact on stumpage earnings and consequently, also on the profitability of timber production.

Figure E14: Rightward shift in timber demand

Recall from ECON1 that a single demand (or supply) curve expresses quantity demanded (or supplied) as a function of price alone whereas the demand (or supply) shifters have remained constant. Mathematically, the timber demand equation can be defined generally as

QD=f(Poutput, ptimber, pother inputs)

 As an empirical example, Toppinen (1998) estimated the demand equation for sawlogs as follows:


            lnQDlogs=1.15lnPsawn wood-1.53lnplogs+2.18lnc

In other words, a rise in the export price of sawn wood, Psawn wood and capital stock (i.e., capacity), c both increased the demand for sawlogs, while a rise in stumpage price, plogs decreased demand.

We can link the mathematical demand equation to the graphical demand curve by noting the effect of price (alone) (i.e., the slope coefficient, determines the shape of the curve) whereas changes in output price and prices of other inputs shift (i.e., change the location of) the curve.

More specifically, it is the marginal productivity (MPP) of timber that determines the shape of the demand curve for timber. The marginal productivity of timber is defined as the addition to forest industry output by using one more units of timber input, when the amount of other inputs is fixed. In the case of derived (input) demand the downward slope is not caused by the diminishing marginal utility, but by the diminishing marginal productivity. When the quantity of timber used increases, marginal productivity of timber decreases. The same principle applies to seedlings as well (Figure E3) so that when the planting density increases, the marginal productivity of seedlings decrease.

Figure E3: Forest owner's (marginal) willingness to pay for seedlings (diagram is step-shaped since the unit for seedlings is an integer package of 10,000 seedlings)

Inputs can alternatively substitute or complement each other. In substitution, the increase in price of one input increases the demand for the other input. For complements, respectively, the increase in price of one input reduces the use of the other input. In Finland, for example, the effects of the domestic wood price on imported volumes have, (interestingly) been found to differ between tree species: imported birch pulpwood (mainly from Russia) has been a complement to domestic wood (Tilli et al. 2001, Mutanen et al. 2004), whereas imported Russian pine pulpwood has substituted domestic wood in the Finnish forest industry (particularly after year 1995) (Tilli et al. 2002).

1. All variables are logarithmic.

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