1. AGEC/FNR 406 LECTURE 11

2. Dynamic Efficiency Two lectures required. Read pages 28-38 of Kahn.

3. Static Efficiency Revisited Static Efficiency is obtained when Net Benefit for one period is Maximized. Is triangle as large as possible? Q P S=MC D=MB

4. Static Efficiency Equilibrium price reflects MB to consumers and MC to producers Demand can be satisfied via production (scarcity is not a problem) Time is not a factor

5. Horizontal Supply Curve Step 3: NB? Producer surplus = 0 Consumer surplus = 1/2 of (8-2)*15 = 45 so NB = 0 + 45 = 45 Q P 15 2 20 8 Step one: demand curve P = 8 - 0.4Q Step 2: supply curve MC =2, constant

6. Exhaustible Resource (e.g. coal) MEC = marginal extraction cost. Assume total available supply = 20 tons. Consumers willing to purchase 15 tons. NB = 45 Q P 15 2 20 8

7. Q P P What if the total supply of ore must be allocated over two periods? Q 12

8. Q P Q P Does this allocation maximize NPV of benefits? Q NB 1 15 5 NB 2

9. Dynamic Efficiency Criteria for efficiency is to maximize present value of net benefits Time is a factor, resource allocation is not independent across time. Supply should be restricted in the current period to provide some stock for the future.

10. Q 8 6 What are net benefits? Q NB 1 = 1/2 of 15*(8-2) = 45 15 5 NB 2 = 0.5*(8-6)*5 + 5*(6-2) = 25 8 22

11. What is the NPV? NB 1 = 0.5*15*(8-2) = 45 NB 2 = 0.5*(8-6)*5 + 5*(6-2) = 25 Now compute NPV: NPV = NB 1 /(1+r) 0 + NB 2 /(1+r) 1 if r = 5% NPV = 45 + 25/1.05 = 45 + 23.8= 68.8

12. Is a NPV of 68.8 the maximum that can be obtained with 20 units of ore, allocated over two periods? No!

13. 4 For example, what about an even allocation to each periods of 10 units? Q Step 1: find price 10 NB = 0.5*(8-4)*10 + 10*(4-2) = 40 8 2 P = 8 -.4*Q P = 8 -.4*10 = 4 Step 2: find NB 1 and NB 2

14. Q 8 4 Step 3: find NPV Q NPV = NB 1 + NB 2 /(1+0.05) 1 10 8 22 4 NPV = 40 + 40 /1.05 = 40 + 38 = 78 > 68.8

15. Is an allocation of 10 + 10 the dynamically efficient allocation? No! To be continued…