1. AGEC/FNR 406 LECTURE 12

2. Static vs. Dynamic Efficiency Static efficiency is obtained when a single period’s net benefits are maximized. Dynamic efficiency is obtained when the present values of net benefits are equal for all periods in a multi-period problem. Dynamic efficiency DOES NOT mean an equal allocation across all periods.

3. Q 8 4 Example, continued Q 10 8 22 4 2. NB = 0.5*(8-4)*10 + 10*(4-2) = 40 1. P = 8 -.4*Q = 4 3. NPV = 40 + 40 /1.05 = 40 + 38 = 78

4. 8 An alternative approach for a two period model Step 1: Graph demand in period 1 20 8. 1.05 22 -0.40 Step 2: Modify period 2 demand and graph it BACKWARDS! -0.40 1.05

5. 8 Step 3: Overlay the graphs 20 8. 1.05 2 2 -0.40 -0.40 1.05

6. Efficient allocation Efficient allocation is where demand curves intersect. P1P1 P2P2 Q1Q1 Q2Q2 10 =10.12

7. Important concepts 20 2MC = 2 = MEC Q P1P1 P2P2 MUC = P - MEC Scarcity rent

8. Numerical Approach Step 1: write down NB in each period NB 1 = benefits - costs = (a-(bQ/2))Q - cQ = 8Q 1 -.2Q 1 2 - 2Q 1 = 6Q 1 -.2Q 1 2 NB 2 = benefits - costs = (a-(bQ/2))Q - cQ = 8 Q 2 -.2 Q 2 2 - 2 Q 2 = 6 Q 2 -.2 Q 2 2

9. Numerical Approach Step 2: Get rid of Q 2 in NB 2 If Q 1 + Q 2 = Q, then Q 2 = Q - Q 1 or Q 2 = 20 - Q 1 so NB 2 = 6(20 - Q 1 )-.2(20 - Q 1 )(20 - Q 1 ) = 120 - 6 Q 1 - 80 + 8 Q 1 -.2 Q 1 2 = 40 +2 Q 1 -.2 Q 1 2

10. Numerical Approach Step 3: Calculate present value of 2-period benefit NPV = NB 1 /(1+r) 0 + NB 2 /(1+r) 1 = 6Q 1 -.2Q 1 2 + (40 +2Q 1 -.2Q 1 2 )/1.05 = 6Q 1 -.2Q 1 2 + 38.095 + 1.905*Q 1 - 0.1905*Q 1 2 = 7.905Q 1 -.3905 Q 1 2 + 38.095

11. Numerical Approach Step 4: Differentiate to find where NPV reaches max Max where dNPV/dQ 1 = 0 or 7.905 - 0.781Q 1 = 0 Q 1 = 10.12 Q 2 = 20 - Q 1 = 9.88 P 1 = 8 -.4*10.12 = 3.95 P 2 = 8 -.4*9.88 = 4.05

12. Numerical Approach NPV = 0.5*(8-P 1 )*Q 1 + (P 1 - 2)*Q 1 +[ 0.5*(8-P 2 )*Q 2 + (P 2 - 2)*Q 2 ]/(1+r) = 0.5*(8- 3.95)*10.12 + (3.95 - 2)*10.12 +[ 0.5*(8-4.05)*9.88 + (4.05-2)*9.88 ]/(1.05) = 78.10

13. Key Points 1. Price = MEC + MUC MUC = 3.95 - 2 = 1.95 2. Under dynamic efficiency Q 1 is lower than under static efficiency, and P 1 is higher. 3. Under dynamic efficiency P 2 is higher than P 1 and Q 2 is lower than Q 1 due to discounting.

14. Extensions 1. Higher discount rate: allocate more to present. 2. Lower discount rate: allocate more to future 3. With zero discount rate, allocations are equal in both periods 4. Greater scarcity reduces allocations in both periods. Without scarcity, MUC = 0