Time Periods • Short-run – all factors (shifters) are held constant, only P and Q change. • Long-run – all factors can shift, defining new relationships between P and Q. • At any given price the quantity of stumpage can change because of factors other than price.
Timber Demand • Specify a time period, usually one year, and a group of buyers, then • Timber demand is the quantities of stumpage that the group would purchase for harvesting at different prices Market demand curve for short-run, i.e. all “shifters” held constant $/MBF P Q MBF/year
Derived Demand for Timber It starts with DLumber and DLogs and DStumpage are derived from DLumber DLumber PLu = $300 Milling & distribution cost = $100/MBF DLogs Plo = $200 Logging & hauling cost = $70/MBF Start with lumber and work back-ward to stumpage DStumpage Q (log scale) Q
Stumpage Supply as a Flow • Flow supply is based on the “flow” of stumpage at a given price, quantity that would actually be sold. • Stock supply is timber inventory in the market area specified, only a small portion of which is actually available at prevailing market prices.
Stock Compared to Flow for Indiana • Sawtimber volume was 17.1 bil. bd. ft. (Doyle) in 1998 (Stock supply) • Sawtimber harvest of industrial roundwood was 367 mil. bd. ft. in 2000 (Flow supply) • Flow was 2.1% of stock
Based on average growth and removals from 1986 to 1997 Doesn’t reflect recent increase in removals
Timber Supply • Specify a time period, usually one year, and a group of sellers, then • Timber supply is the quantities of stumpage that forest owners would sell for harvest at different stumpage prices $/MBF P SStumpage MBF/year Q
Supply of Stumpage Determines Supply of Lumber $/MBF SLu 300 Milling & distribution cost = $100/MBF SLo 200 Logging & hauling cost = $70/MBF SS 130 Start with stumpage and work backward to lumber MBF/year log scale Q
Timber Supply as Aggregate of Individual Supply Curves For a given price sum quantities horizontally $/MBF SstumpTtotal stumpage supply curve SstumpB for timber owner Bob SstumpJ for timber owner Jane 500 100 MBF log scale 150 300 50 150 100 200 Price of $100/MBF Price of $500/MBF
Competition from Stumpage Buyer’s Perspective • Highly competitive stumpage market • Small mill is price taker • Large mill • Monopsonist – one buyer • Oligopsonist – very few buyers $/MBF Ss Eps > 1 elastic MBF $/MBF Ss Eps < 1 inelastic MBF
Short-Run Equilibrium $/MBF SLu 300 DLu SLo 200 DLo SS 130 DS MBF/year log scale Q
Efficiency of Stumpage Market • Theory is that buyer pays same price for all the stumpage it purchases • Price based on intersection of Ss and Ds
Efficiency of Stumpage Market • Example • Mill buys 12,000 MBF @ $200/MBF • Total cost is $2,400,000 • Mill wants to increase output, need to buy 14,000 MBF. • Must increase price to $250/MBF • Total cost is $3,500,000 • Increase in total cost is $1,100,000 • Marginal cost is ΔVC/ Δ Q, • $1,100,000/2,000 = $550/MBF • MC isn’t $250 - $200 = $50
Efficiency of Indiana’s Stumpage Market • Stumpage markets are segmented by • Average quality of timber stand, and • How timber is sold • Sealed bid, usually with a consulting forester conducting the sale (highest price) • One-on-one negotiation between single buyer and timber owner (lower price) • Owner accepts first offer made by buyer (lowest price)
Efficiency of Indiana’s Stumpage Market • What are implications of this price discrimination? • To forestland owner • To mills