Question

Bell-land has 10 households. They can earn income by either weaving baskets or fishing. Because the lake has a limited number of fish, the more they fish the less each person catches. In particular, if nhouseholds fish in the lake, then each fishing household makes an amount

                       Ih = 12 – 2n

Ih : daily income of the household measured in dollars

If a household decides to weave it makes $2

Assume each household makes the decision of whether to weave baskets or fish in the lake independently. How many households do you expect to fish every day? How many to weave baskets?

Calculate the total income of the village in the above equilibrium?

Show that when only 3 households fish in the lake the total income is larger than the one you found in part B

If the villagers together decided to achieve the allocation in part c, what kind of rules would be needed to institute it?

If they wanted everyone to benefit equally in the new system, what kind of tax and transfer would they need?

What type of good is the fishery? What characteristics make it that good?

Answer 1

Answer: -

(A). Households would choose to fish as long as they got at least as much revenue from fishing as from basket-weaving. In this case, until $12 - 2n = $2, or until n=5 fishers. There would also be 10-5=5 weavers. Everyone earns $2, so village income is $2*10 = $20.

(B). If 3 families fish, the waves of a fisher are 12-2*3 = $6. These three fishers earn $18, and the 7 weavers earn 14, for a total village income of $32. However, we are prevented from staying at this outcome if everyone behaves independently: one of the weavers would notice that he could switch to fishing, and the wage with 4 fishers is $4, better than weaving --- so he would indeed make the switch.

(C). If we wanted to achieve this outcome, we would need to tax each fisher $2.80 and compensate each non-fisher $1.20. This gives each person a net benefit of either $6-$2.80 = $3.20 or 2 + $1.20 = $3.20, so there's no incentive for weavers to change into being fishers.

(D). The fishery is a "common good", because it is non-exclusionary (anyone can access it), but it is rivalrous (meaning that one person's benefit is reduced by other people using it.)