Final Answer:
Prospect theory is a behavioral economic theory that describes the way people choose between probabilistic alternatives that involve risk, where the probabilities of outcomes are known. The theory states that people make decisions based on the potential value of losses and gains rather than the outcome and that people evaluate these losses and gains using certain heuristics.
The correct option is 3)
Step-by-step explanation:
One of the key components of prospect theory is the value function which describes how individuals evaluate gains and losses. This function is distinct because it is defined with the following characteristics:
- The function is steeper for losses than gains, indicating loss aversion (losses hurt more than gains please).
- The function is concave for gains, which implies diminishing marginal utility for gains (as wealth increases, the added utility from an additional dollar decreases).
- The function is commonly convex for losses, reflecting increasing marginal disutility as losses grow.
- The value function is typically steeper for losses than for gains, reflecting loss aversion.
Given these characteristics for gains (x>0), the correct utility function shows a concave shape, meaning it would increase as x increases but at a decreasing rate. Out of the given options, the only function that is concave for gains is the natural logarithm function, which increases at a decreasing rate as x increases and approaches infinity.
Therefore, the correct answer is: 3) U(x) = ln(x)