# Investing in the Agent's Productivity

### Abstract

A principal-agent problem of the hidden-effort variety is studied in which the productive outcome is specified as the product of two control variables, effort and productivity. Productivity is determined by investments in the productive system on which the agent brings to bear his effort. Three situations are compared: in the first one not only gross output of the agency is assumed contractible but also the productivity-enhancing investment. In the second situation the agent decides on how to equip himself while the principal sees only the outcome net of the productivity-enhancing cost. In the third situation an additional agent takes care of productivity. The model is of the LEN type but with logarithmic cost functions instead of the common quadratic specification. Quadratic cost functions together with the multiplicative specification of productive output would not allow for well-defined optimization problems.