Question

You both want a good grade, but you don't like to work. If you both work hard, you'll both receive an A, giving you a happiness of 40 "utils". If only one works, you will receive a B and a utility of 30 . If no one works, both will receive a D, and a happiness of 10 . The cost of effort is 25 utils. What is the most likely outcome? 7.

A. Use the data from problem 6. If you could collaborate on several homeworks throughout the quarter, instead of just one, Could your answer to 6 change?
B. Use the data from problem 6 . We find a classmate who cares about good grades: a B gives her a happiness of 50 and an A of 80 . If this classmate were your partner, Would your answer of 6 change? 9. Use the data from problem
C. Would you like to work with her?
Use the data from problem

Answer 1

The most likely outcome for a single homework collaboration is for neither student to work, resulting in the lowest net utility but highest per utility without effort. When considering multiple homework opportunities, the answer might change due to the benefits of cooperation. The presence of a more grade-conscious classmate changes the incentive structure, potentially making it advantageous to collaborate to achieve higher grades and utilities.

Step-by-step explanation:

Evaluating Outcomes Given Utilities and Costs

Based on the scenario provided, where different efforts result in different utility outcomes and grades, we can use the concept of net utility to determine the most likely outcome. If both students work hard, each receives an A grade with a utility of 40 utils, but incur a cost of effort of 25 utils. The net utility would then be 15 utils (40 utils happiness - 25 utils effort cost). However, if only one student works, they both get a B which provides 30 utils without any effort cost, resulting in a net utility of 30 utils. If neither works, they receive a D with a happiness of 10 utils and no cost, leading to a net utility of 10 utils. On its own, the rational choice for a one-time interaction with these payoffs would be for neither student to work, accepting a D and 10 utils.

When we consider multiple homework opportunities (collaborating on several homeworks throughout the quarter), the answer could potentially change due to the possibility of building a cooperative relationship where the effort cost might be mitigated by a consistent high utility outcome, incentivizing sustained effort.

If a third classmate, who values grades even higher, is introduced into the scenario, with a B giving her 50 utils and an A 80 utils, working with this classmate could change the outcome. The higher valuation on grades could lead to a scenario where the cost of effort is outweighed by the potential for higher utility, particularly if the classmate's study efforts increase the likelihood of receiving higher grades. Therefore, it might make strategic sense to partner with her.