The table below provides information about costs and benefits from the production of
pesticides that pollutes a lake used by a trout farmer
TP of pesticides/
week
Pesticides
producer Mc
Marginal external
costs
Marginal Social
benefits
0 0 0 250
1 5 33 205
2 15 67 165
3 30 100 130
4 50 133 100
5 75 167 75
6 105 200 55
7 140 233 40
If no one owns the lake and if there are no regulation of pollution, what is the quantity
of pesticides produced per week and what is the marginal cost of pollution borne by
the trout farmer
b) If the trout farm owns the lake, how much pesticides is produced per week and what
does the pesticides producer pay the farmer per tonne
c) If the pesticides producer owns the lake, and if a pollution free lake rents for $100 a
week, how much pesticides is produced per week and how much rent per week does
the farmer pay the pesticides producer for the use of lake
d) Compare the quantities of pesticides in parts b and c and explain the relationship
To answer these questions, we need to understand the concept of marginal external costs and marginal social benefits. Marginal external costs are the costs imposed on third parties not involved in the production or consumption of a good, such as pollution. Marginal social benefits, on the other hand, refer to the additional benefits to society from producing one more unit of a good.
a) If no one owns the lake and there are no regulations, the quantity of pesticides produced would be determined by the producer based on their own costs and benefits. Looking at the table, we can see that when 3 units of pesticides are produced per week, the marginal external cost is equal to the marginal social benefit, which is 130. Therefore, the quantity of pesticides produced per week would be 3, and the marginal cost of pollution borne by the trout farmer would be 130.
b) If the trout farm owns the lake, they would consider the costs and benefits of pesticide production, including the pollution it creates. The trout farm would want to minimize the pollution that affects their trout production. In this case, they would only allow pesticide production if the marginal cost of pollution is less than or equal to the marginal benefit they receive from the pesticides. Looking at the table, we can see that when 1 unit of pesticide is produced per week, the marginal external cost is equal to the marginal social benefit, which is 205. Therefore, the quantity of pesticides produced per week would be 1, and the pesticides producer would pay the trout farmer 205 per tonne of pesticides.
c) If the pesticides producer owns the lake, they would consider the costs and benefits of both pesticide production and renting out the lake. They would want to maximize their profit, which includes the rent they receive from the trout farmer. In this case, the pesticides producer would only allow pesticide production if the marginal cost of pollution is less than or equal to the rent they receive. Looking at the table, we can see that when 5 units of pesticides are produced per week, the marginal external cost is equal to the rent, which is 75. Therefore, the quantity of pesticides produced per week would be 5, and the rent per week the farmer pays the pesticides producer for the use of the lake would be 75.
d) Comparing the quantities of pesticides in parts b and c, we can see that when the trout farm owns the lake, they produce only 1 unit of pesticides per week. However, when the pesticides producer owns the lake, they produce 5 units of pesticides per week. This difference is due to the different incentives the two parties have. The trout farm, as the owner of the lake, wants to minimize pollution for the benefit of their trout farming. On the other hand, the pesticides producer, as the owner of the lake, wants to maximize their profit, taking into account both pesticide production and rent. As a result, the quantity of pesticides produced is higher when the pesticides producer owns the lake compared to when the trout farm owns it.