Components of Fishermen's Utility in the Weevokil Model

Definition of Marginal External Cost in the Weevokil Banana Model

A group of fishermen earns income from two sources: a fixed salary from part-time work, and profits from fishing in a local river. A nearby banana plantation's production (represented by quantity Q) pollutes the river, which directly reduces the fishermen's profits from fishing. As the plantation produces more bananas, the pollution worsens, and fishing profits decrease at an increasing rate. Which of the following utility functions, U(Q), most accurately models the fishermen's overall well-being based on this situation?

Modeling Utility with Externalities

Constructing a Utility Function with an Externality

Harvest Shortfall and Price Impact

Within a model where fishermen's well-being is negatively impacted by pollution from banana production (Q), a valid way to represent their utility is as a single, unified function that increases with Q, assuming that greater banana output also boosts the overall local economy, benefiting the fishermen indirectly.

The utility (overall well-being) of a group of fishermen is modeled by the function U(Q) = 5000 - 2Q^2, where Q is the quantity of bananas produced by a nearby plantation. Match each term from this model to its correct description.

An independent farmer, who keeps all the food she produces, is trying to decide how many hours to work. At her current choice of 16 hours of free time and 9 bushels of grain, she determines two things: 1) She would be willing to give up 4 bushels of grain for one more hour of free time. 2) Her production schedule shows that if she works one hour less (gaining one hour of free time), her grain output will fall by only 3 bushels. Based on this information, what should the farmer do to increase her overall satisfaction?

Justifying the Structure of a Utility Function with an Externality

A community of shrimpers' overall economic well-being (utility) is negatively affected by the output (Q) of a nearby coastal factory. Their utility is modeled by the function U(Q) = 25,000 - 10Q^2. In this model, what is the economic interpretation of the component 25,000?

A community of fishermen's overall well-being (utility) is modeled by the function U(Q) = 50,000 - 4Q^2, where Q represents the tons of output from a nearby chemical plant that pollutes their fishing grounds. Initially, the plant produces 20 tons of output. Due to new environmental regulations, the plant reduces its output to 15 tons. What is the resulting change in the fishermen's total utility?