Suppose paul's preference over his income can be presented by a
NMUF µ:;XX where X is Paul’s income in 1000 euros. In his current job he earns 50,000 euro/year. He is offered a job that pays him 64000euro or 36000 with equal probability. Is Paul willing to change job?
To determine if Paul is willing to change jobs, we need to compare his utility (preference) function for his current income with the expected utility of the new job options.
Given that Paul's preference over his income can be presented by a NMUF µ:;XX, we assume that he has a concave utility function, meaning that he experiences diminishing marginal utility of income.
Let's calculate the expected utilities for the two job options:
1. Job that pays 64000 euro:
Expected utility = 0.5 * µ(64000) + 0.5 * µ(50000)
= 0.5 * utility at 64000 + 0.5 * utility at 50000
2. Job that pays 36000 euro:
Expected utility = 0.5 * µ(36000) + 0.5 * µ(50000)
= 0.5 * utility at 36000 + 0.5 * utility at 50000
If the expected utility from either of the new job options is greater than the utility from his current job, Paul would be willing to change jobs.
However, without specific information about the utility function µ and its specific properties (such as concavity and curvature), we cannot definitively determine if Paul is willing to change jobs based on the provided information.