AGEC/FNR 406 LECTURE 11

Dynamic Efficiency Two lectures required. Read pages of Kahn.

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

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

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

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

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

Q P Q P Does this allocation maximize NPV of benefits? Q NB NB 2

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.

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

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 = /1.05 = = 68.8

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

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)* *(4-2) = P = 8 -.4*Q P = 8 -.4*10 = 4 Step 2: find NB 1 and NB 2

Q 8 4 Step 3: find NPV Q NPV = NB 1 + NB 2 /(1+0.05) NPV = /1.05 = = 78 > 68.8

Is an allocation of the dynamically efficient allocation? No! To be continued…