1. Dynamic Efficiency and Mineral Resources Monday, Feb. 27

2. 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

3. 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

4. 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.

5. 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

6. 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.

7. 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

8. 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?

9. 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.