Final answer:
Robinson and Friday's endowment points and indifference curves can be graphically represented based on their initial resource ownership and identical homothetic preferences. Initially, their trades are balanced but a proposed project by Robinson leads to a trade surplus for Friday and a trade deficit for Robinson.
Step-by-step explanation:
Robinson and Friday are two agents with different levels of endowments in coconuts and bananas and identical homothetic preferences. Their endowment points can be represented on a graph where coconuts are on the x-axis and bananas on the y-axis. Robinson's endowment point would be at (8 coconuts, 2 bananas) and Friday's at (2 coconuts, 8 bananas).
To represent their indifference curves, we would sketch curves that represent combinations of coconuts and bananas that provide them with the same level of utility. Because they have identical demand functions, these curves would be similar in shape but located differently on the graph, centered around their respective endowment points. The shape of the curves would reflect the trade-off each agent is willing to make between coconuts and bananas, with the shape being consistent due to their homothetic preferences.
If we incorporate the scenario where Robinson and Friday trade goods and services, initially, their trades would be balanced because they value their exchanges equally. However, once Robinson proposes a trade imbalance, where he receives goods now and pays back later from the extra produce of his irrigated garden, the balanced trade scenario changes. This introduces a trade surplus for Friday and a trade deficit for Robinson.