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# Class 5

Class 5. Dynamic Efficiency. Reference source for the slides: http://www.agecon.purdue.edu/staff/shively/courses/AGEC406/index.htm. Static vs. Dynamic Efficiency. Static efficiency is obtained when a single period’s net benefits are maximized.

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## Class 5

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### Presentation Transcript

1. Class 5 Dynamic Efficiency Reference source for the slides: http://www.agecon.purdue.edu/staff/shively/courses/AGEC406/index.htm

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

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

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

6. Efficient allocation Efficient allocation is where demand curves intersect. P1 P2 10 • • =10.12 Q1 Q2

7. Important concepts P1 P2 MUC = P - MEC 2 MC = 2 = MEC Q 20 20 Scarcity rent

8. Numerical Approach Step 1: write down NB in each period NB1 = benefits - costs = (a-(bQ/2))Q - cQ = 8Q1-.2Q12 - 2Q1 = 6Q1-.2Q12 NB2 = benefits - costs = (a-(bQ/2))Q - cQ = 8 Q2 -.2 Q22 - 2 Q2 = 6 Q2 -.2 Q22

9. Numerical Approach Step 2: Get rid of Q2 in NB2 If Q1 + Q2 = Q, then Q2 = Q - Q1 or Q2 = 20 - Q1 so NB2 = 6(20 - Q1)-.2(20 - Q1)(20 - Q1) = 120 - 6 Q1 - 80 + 8 Q1 -.2 Q12 = 40 +2 Q1 -.2 Q12

10. Numerical Approach Step 3: Calculate present value of 2-period benefit NPV = NB1/(1+r)0 + NB2/(1+r)1 = 6Q1-.2Q12 + (40 +2Q1 -.2Q12 )/1.05 = 6Q1-.2Q12 + 38.095 + 1.905*Q1 - 0.1905*Q12 = 7.905Q1 - .3905 Q12 + 38.095

11. Numerical Approach Step 4: Differentiate to find where NPV reaches max Max where dNPV/dQ1 = 0 or 7.905 - 0.781Q1 = 0 Q1 = 10.12 Q2 = 20 - Q1 = 9.88 P1= 8 - .4*10.12 = 3.95 P2 = 8 - .4*9.88 = 4.05

12. Numerical Approach NPV = 0.5*(8-P1)*Q1 + (P1 - 2)*Q1 +[ 0.5*(8-P2)*Q2 + (P2 - 2)*Q2 ] /(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 Q1 islower than under static efficiency, and P1 ishigher. 3. Under dynamic efficiency P2 ishigher than P1 and Q2 islower than Q1 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

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