Hotelling Rule Resource Price Calculator
Apply Hotelling's rule to find the optimal price path for an exhaustible resource.
Shows how the royalty grows at the rate of interest over time.
Hotelling’s rule (1931) is the central result of exhaustible resource economics. It states that the net price (royalty) of a non-renewable resource must grow at the rate of interest in a competitive equilibrium:
dP/dt = r * P_net
where P_net = price - marginal extraction cost and r is the real interest rate.
The intuition is an arbitrage argument. A resource owner compares two options: extract now and invest the proceeds, or leave the resource in the ground and sell later at a higher price. In equilibrium, both options must yield the same return. If the price grew faster than r, owners would delay extraction; if slower, they would rush to extract. The equilibrium is exactly r-percent growth.
Price at time t:
P(t) = c + (P_0 - c) * e^(rt)
where c is the marginal extraction cost, P_0 is today’s price, and (P_0 - c) is today’s royalty (scarcity rent).
Practical limitations. Real resource prices do not follow Hotelling paths cleanly. Technological change lowers extraction costs over time. New discoveries increase the known stock. Demand substitution (e.g. renewables replacing oil) compresses the royalty. This is why oil prices have been trendless in real terms over the 20th century despite Hotelling’s elegant theory.
When it does apply. The rule works best for resources with well-defined stocks, no close substitutes, and competitive markets. Groundwater depletion, phosphate rock, and certain rare earth elements are better candidates than oil or natural gas.