G16 is an essential reading. It provides a starting point for our model. The main complication is that, the agent has nonlinear utility over the payment. So how the payments are distributed over time matters a great deal. As a consequence, we cannot reduce the firm’s payoff to the function of virtual surplus—we must account of the non-transferability of the the firm’s cost to the agent.
Technically, we need to derive two conditions to guarantee IC and IR constraints: envelope and monotonicity. The envelope condition shows that each type should derive the premium beyond the low type for truthtelling. The premium consists of two terms: the weighted rents for his information advantage, and the gap to ensure within-period truthtelling. The monotonicity condition ensures that the net present value of the cash flow increases in the current type. The envelope condition puts constraints the payment scheme, while the monotonicity condition restricts the cash flow policy.
Once these two conditions are in place, we can apply the variational approach to derive sharp insights. In particular, we focus on the inefficiency loss, i.e., the distortion from the first best. The dynamics of the distortion depends on the interplay of risk aversion and market volatility. Depending on how they play out, the distortion can go either way. This property allows us to explain a wide range of salesforce practices.