Question

The government is considering the use of a policy to increase the adoption of a beneficial management practice (BMP) that will have implications for landowners and society. The costs of the BMP to the landowner is $15,000 right away and $2,000 each subsequent year starting at the end of year 1. The BMP also generates public goods and these public benefits are valued at $3,250 per year starting right away. The public costs of the BMP are estimated to be $250 per year starting right away.

a) Assume the discount rate is 5% and the timeframe for analysis is 25 years. Where would this BMP fall on Pannell’s Private-Public Benefits Framework and which policy option would you recommend? (15 points)

b) Now assume the discount rate is 10% and the timeframe stays the same at 20 years. Use Pannell’s Private-Public Benefits Framework to recommend a particular policy option. (15 points)

Answer 1

1. Beneficial management practice(BMP) will lie in the A panel of public private benefits framework where public benefits are exceeding the private cost. . Due to this, there will be positive incentives, and it is recommended to choose that benefit management policy which generates positive incentives.

2. With the rise in discount rate and the time frame being 20 years, in this case also there will be no positive incentives for this management practice because it is lying in F panel where private cost is exceeding public benefits where technological development is recommended.   

Step-by-step explanation

1. Cost of BMP to the landowner is $15000 and $2000 each subsequent year.

Time(t) = 25 years

Public benefit= $3250 per year and public cost = $250 per year .

Discount rate(i) is 5%.

Net present value(NPV) = ∑ t=0 to 25 (benefit - cost) / (1+i)^t

Or we can use= a( 1-r^n)/ (1-r)

where i is a discount rate, and r is a common ratio .

For a public good-

NPV = (3250-250)/ ( 1+ 0.05)^0 + (3250-250)/ ( 1+ 0.05)^1 + (3250-250)/ ( 1+ 0.05)^2 +.........+ (3250-250)/ ( 1+ 0.05)^24

Or 3000/(1+ 0.05)^0 + 3000/(1+ 0.05)^1 + ........+ 3000/(1+ 0.05)^25

Common ratio r = 1/1+i = 1/ 1.05

3000/ [ 1-1/1.05] * [1 - {1/1.05}^24]

3150/ 0.05* [ 1- {1/1.05}^24]  

= $43465.72

For the landowner -

NPV= 2000 / (1.05)^1+ 2000 / (1.05)^2 + 2000 / (1.05)^3 +................+ 2000 / (1.05)^25

= 28187.89

For the landowner $15000 is the right away cost, add 15000 to NPV for 25 years

Total NPV for the landowner = 15000 + 28187.89

= $43187.89

Since the NPV of public goods is greater than the landowner, then according to a public private benefit framework, it will lie in the A panel of the framework. A panel contains those management policies where public benefits outweigh private costs since public net benefits are greater than there will be positive incentives for the use of this management policy . It is recommended that if landlords do not adopt land use changes without positive incentives, then that policy is not suitable, and if private cost exceeds the public goods, there will be no positive incentives. That management policy is chosen that generates positive incentives.

2. Now, the discount rate is 10%, and time is 20 years .

NPV for the landowner -

2000 / (1.1)^1+ 2000 / (1.1)^2 + 2000 / (1.1)^3 +................+ 2000 / (1.1)^25

= $18154.08

Add $15000 right away cost to $18154.08

Total NPV of the landlord = $33154.08

NPV for a public good -

  a( 1-r^n)/ (1-r)

where i is a discount rate, and r is a common ratio .

3000/(1+ 0.1)^0 + 3000/(1+ 0.1)^1 + ........+ 3000/(1+ 0.1)^24

3000 / [ 1-1/1.1] * [1 - {1/1.1}^24]

3300/ 1.1 * [ 1-{1/1.1}^24]

33000* 0.8984

= $29649.65

In this case also, the NPV of the landowner is greater than that of a public good, then it will lie in an F panel where we cannot use positive incentives ,that is, private cost exceeding public benefits. Technological development is recommended to create better environmental policies and options that can be adopted regardless of the incentives.