AGEC/FNR 406 LECTURE 11

Dynamic Efficiency

Two lectures required.

Read pages 28-38 of Kahn.

Static Efficiency Revisited

Static Efficiency is obtained when Net Benefit for one period is Maximized.

Is triangle as large as possible?

Q

PS=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 = 0 + 45 = 45 Q

P

15

2

20

8

Step one: demand curve

P = 8 - 0.4Q

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

15

2

20

8

Q

P P

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

Q

1 2

Q

P

Q

P

Does this allocation maximize NPV of benefits?

Q

NB1

15 5

NB2

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

NB1 = 1/2 of 15*(8-2) = 45

15 5

NB2 = 0.5*(8-6)*5 + 5*(6-2) = 25

8

22

What is the NPV?

NB1 = 0.5*15*(8-2) = 45

NB2 = 0.5*(8-6)*5 + 5*(6-2) = 25

Now compute NPV:

NPV = NB1 /(1+r)0 + NB2 /(1+r)1

if r = 5%

NPV = 45 + 25/1.05 = 45 + 23.8= 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)*10 + 10*(4-2) = 40

8

2

P = 8 - .4*Q

P = 8 - .4*10 = 4

Step 2: find NB1 and NB2

Q

8

4

Step 3: find NPV

Q

NPV = NB1 + NB2 /(1+0.05)1

10 10

8

22

4

NPV = 40 + 40 /1.05 = 40 + 38 = 78 > 68.8

Is an allocation of 10 + 10 the dynamically efficient allocation?

No!

To be continued…