Department of Economics Roma Tre University Academic year: 2014-2015 Natural Resource Economics Instructor: Prof. Luca Salvatici [email protected] Natural Resource Economics - a.a.2014/15 Lecture 20 Nonrenewable resources: – Extraction costs – Excel exercises Natural Resource Economics - a.a.2014/15 Extraction costs: optimal control model T max y ,T , A Π [y ] = ∫ ( py − ( ay + cy 2 )) e − rt dt 0 . x = − y , x ( 0 ) = S , x (T ) = A ≥ 0 1. 2. 3. 4. Assume A = 0: write the current value Hamiltonian Derive the FOCs What is going to be y*(T)? Draw the marginal and average cost curves Economia delle risorse naturali - a.a. 201011 3 FOCs ∗ ∗ μ 2 μ 0 0 0 ∗ 0 ∗ ∗ ∗ ∗ ∗ =0 0 0 Natural Resource Economics - a.a.2014/15 FOCs Natural Resource Economics - a.a.2014/15 What is going to be y*(T)? Natural Resource Economics - a.a.2011/12 6 Marginal and average costs Economia delle risorse naturali - a.a. 201011 7 Optimal control Economia delle risorse naturali - a.a. 201011 8 Optimal control: graph y≤4 Economia delle risorse naturali - a.a. 201011 9 Discrete time version 2-2sol.xls Natural Resource Economics - a.a.2014/15 EXCEL example: extraction costs • Mineral stock: X(0) = 1 and ten years from now the mine is going to be taken by the Government • Find the optimal extraction path (Y*(t), t = 0, 1, …, 9) to maximize the present value of the following profit function: Parameters: Mineral Price p = 1 = prezzo del minerale c = 0.5 = average extraction cost δ = 0.05 = interest rate π t =    p − cY X (t )  (t )  Y (t ) Natural Resource Economics - a.a.2014/15 11 EXCEL example: solution  0,5Y (t )   Max∑ 0,95 1 − Y (t )  X (t )  t =0   subX t +1 = X t − Yt 9 t What if there was a salvage value? compito1-Es3.xls Natural Resource Economics - a.a.2014/15