Question

"In the initial scenario, when Charles' utility is defined as U(e) = pL + (1 - p)we - c(e), derive the first order condition with respect to effort (e). How does this relate to his effort optimization?

Analyze how the parameters p and L affect Charles' effort (e) in the initial utility function. Provide an intuitive explanation for these effects.

In the scenario where Charles adopts an expectation as a reference point in his utility function, what is the first order condition with respect to effort (e)? Consider different cases where L > we, L < we, and L = we. How does the function v(x) affect this condition, and why does it make sense?

Assuming L > we, explain the first order condition for effort (e) when Charles has an expectation as a reference point in his utility function.

Explain the first order condition for effort (e) when L < we in the scenario where Charles has an expectation as a reference point in his utility function.

In the case where L = we, derive the first order condition for effort (e) with an expectation as a reference point in his utility function.

How does the parameter p influence Charles' effort in the scenario with an expectation as a reference point? Provide an intuitive explanation for this relationship.

Analyze whether effort is increasing or decreasing in L when Charles adopts an expectation as a reference point. Explain the intuition behind this.

In Gneezy et al. 2017, the authors conducted experiments with varying L and p. Compare their findings with the relationships between effort, L, and p that you've identified in the above questions. Are the experimental results consistent with the theoretical analysis?"

Answer 1

The first order condition for effort in Charles' utility function indicates the effort level that maximizes his expected utility. The parameters p and L influence his willingness to exert effort by affecting the trade-off between the likelihood of loss and the security of the potential payout. Gneezy et al. 2017 experiments may affirm theoretical predictions if they show effort correlates with varying levels of fear of loss and comfort with a safety net.

Step-by-step explanation:

When analyzing Charles' utility function U(e) = pL + (1 - p)we - c(e), where U is utility, e is effort, L is the payout for loss, we is the wage if effort leads to employment, p is the probability of loss, and c(e) is the cost of effort, the first order condition (FOC) is found by taking the derivative of the utility function with respect to effort and setting it equal to zero. The FOC represents the value of effort that maximizes Charles' expected utility.

The parameters p and L significantly influence Charles' effort. A higher p (probability of loss) reduces the component of utility derived from employment wages, thus making the loss component more significant. This might incentivize more effort if loss-aversion is strong. Conversely, a higher L increases the safety net in case of loss, which could either lead to more effort due to increased security, or less effort if the safety net is sufficient to lower the value of additional wages from effort.

In the scenario where Charles adopts an expectation as a reference point in his utility, for cases where L > we, L < we, and L = we, the FOC adapts to consider the difference between the actual outcome and Charles' reference point. The function v(x) in the utility function quantifies the value he assigns to gains or losses relative to his expectations.

In Gneezy et al. 2017, the authors conducted experiments with varying L and p. If their findings indicate that effort increases with higher p and lower L, it would suggest that the fear of loss motivates effort. If effort decreases with higher p and higher L, it may reveal a comfort with the safety net that reduces the incentive to exert maximum effort. These outcomes would be consistent with the loss aversion and safety net theories in behavioral economics.