Roberta Lives Alone on a Deserted Island

question 39

Essay

Roberta lives alone on a deserted island. She can spend her time gathering coconuts or bananas. She has 16 hours available each day and can gather 4 coconuts in an hour or 8 bananas in an hour. Diagram Roberta's budget constraint. Given that Roberta's Marginal Utility of bananas is always 25 and her Marginal utility of coconuts is always 100, what is her optimal consumption? One day an individual from a neighboring island arrives by boat and offers to exchange any number of fruits at a rate of 1 coconut for 1 banana. Diagram Roberta's budget constraint at this exchange rate assuming she will now spend all her time gathering bananas. Is Roberta better off? What does she consume?

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Definitions:

ATP

Adenosine triphosphate, a molecule that stores and transfers energy within cells, acting as a universal energy currency for cellular processes.

Laws of Physics

The laws of physics are the fundamental principles that describe the behavior of the physical universe, including concepts of energy, motion, forces, and matter interactions.

Sunlight

the light and energy that comes from the sun, essential for photosynthesis in plants and influencing Earth's climate and weather.

Second Law

Also known as the second law of thermodynamics, it states that the total entropy of an isolated system can never decrease over time, and is central to the direction of heat transfer and the efficiency of heat engines.