Dynamic Efficiency and Mineral Resources Monday, Feb. 27
Mineral extraction decisions • Private property rights • Owner will extract that amount of resource that maximizes her net returns over time. • Rent – accrues to owner of resource because of scarcity
Natural Resource Rent In our previous example (two-period, social planner model), rent was viewed as all returns going to society. Period t0 $ Rent MB 3.905 MC Wages, etc. Quantity 10.238
Formal definition of rent: • Returns to a resource in excess of what is required to bring the resource into production. • e.g. any earning above extraction cost for minerals • In formal sense, must have a market and a PRICE to have rent.
Natural resource rent to resource owner When a resource is privately owned, the owner earns rent. The remaining surplus accrues to consumers. Consumer surplus Period t0 $ Rent (producer surplus) MB 3.905 MC Wages, etc. Quantity 10.238
Dynamic efficiency and mineral extraction • In a well-functioning market, a mineral owner’s incentives lead to a rate of extraction that satisfies: • MNB0 = PVMNB1 = … = PVMNBt • This maximizes the present value of rents to the owner of the resource. • Rents to owner reflect user costs to society • If owner doesn’t make decision based on earning rent, then opportunity costs of current use are ignored.
Marginal rent to resource owner is equal to marginal user cost to society MUC = 1.905 Marginal rent = 1.905 Period t0 $ Total rent = 1.905*10.238 MB = 59.41 3.905 MC MEC + MUC = P Quantity 10.238
Exercise – how a market allocation of a depletable resource responds to various factors • Illustrate dynamically efficient extraction rate and marginal user costs • How does the availability of a renewable substitute affect extraction rate? (A more sustainable solution?) • How do increasing marginal extraction costs affect extraction rate? • Can investment of rents also address sustainability?
In a two-period world: MNB0 = PBMNB1 MB = 8 - .4q MEC = $2, r=.1 Total Q = 20 = q0+ q1 Solve for qs 2 equations, 2 unknowns In an unlimited time frame: MNB0 = PBMNB1 =…= PVMNBt MB = 8 - .4q MEC = $2, r=.1 Total Q = 20 = q0+ q1+…+ qt Solve for qs t equations, t unknowns Computer algorithms use iterative process to solve for qs.