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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**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. 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.**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**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**Step 3: Overlay the graphs**8 8 . 1.05 -0.40 1.05 -0.40 2 2 20 20**Efficient allocation**Efficient allocation is where demand curves intersect. P1 P2 10 • • =10.12 Q1 Q2**Important concepts**P1 P2 MUC = P - MEC 2 MC = 2 = MEC Q 20 20 Scarcity rent**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**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**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**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**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**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.**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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