Wealth Effects When the Cost of Effort is Money
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We study the effects of the agent’s wealth on the agency cost and the principal’s profit in the principal-agent model in which the agent’s effort entails a monetary cost. We show that if the inverse of the marginal utility function is concave in the utility function, then an increase in the agent’s wealth lowers the agency cost for any effort level, directly implying that the principal clearly benefits from such a decrease in the agency cost. However, even if the convexity of the marginal utility function with respect to the utility function is assumed, as in most of the previous results, the effects of the agent's wealth on the agency cost remain unclear in our model. The main reason is because a rise in wealth inevitably makes the incentive problem easier by lowering the marginal cost of effort, reducing the agency cost whereas that convexity raises the agency cost.
Abstract
We study the effects of the agent’s wealth on the agency cost and the principal’s profit in the principal-agent model in which the agent’s effort entails a monetary cost. We show that if the inverse of the marginal utility function is concave in the utility function, then an increase in the agent’s wealth lowers the agency cost for any effort level, directly implying that the principal clearly benefits from such a decrease in the agency cost. However, even if the convexity of the marginal utility function with respect to the utility function is assumed, as in most of the previous results, the effects of the agent's wealth on the agency cost remain unclear in our model. The main reason is because a rise in wealth inevitably makes the incentive problem easier by lowering the marginal cost of effort, reducing the agency cost whereas that convexity raises the agency cost.