Question

a small indigenous village is situated along the bank of a river. for this year, they need to decide how much water to collect from the river for irrigation purposes. the amount of water that is collected this years has no bearing on the amount of water that they can collect in the future years form the river. marginal social benefits from the water are given by MSB=20-q/2 and marginal social scosts from collecting the water are given by MSC=2+q

a) graph the MSB curve

b)what are the total benefits or increasing the amount or irrigation water collected from 10 units to 20 units

c) graph the MSC curve

d) what are the total costs of increasing the amount or irrigation water collected from 5 units to 15

e) what is the efficient level of water collection (q*) from the river this year?

f) at q* what are the total benefits, total costs, and net benefits

Answer 1

b) If MSB is 20-q/2, to find the total social benefits, we have to integrate it. Therefore TSB=20q-q²/4. At q=10, TSB=175. At q=20, TSB=300. Therefore the increase in TSB is 125.

d) Similarly integrating MSC, we get TSC=2q+q²/2. At q=5, TSC=22.5. AT 15, TSC=142.5. Increase in TSC=120.

e) For finding the efficient level, we need to equate MSB and MSC. Equating them 20-q/2=2+q. This implies q*=12.

f) At q=12, TSB=204. TSC=96. Net benefits are 108.

For parts a and c, see image.