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Additional resources for Advances in Economics and Econometrics: Theory and Applications, Eighth World Congress, Volume III (Econometric Society Monographs)
This is because a high p generates a low R and this improves incentives. In such situations it may be optimal to raise p all the way to its maximum, that is, to p1 . 29 However, it is easy to see that it will never be optimal for p to exceed its social welfare maximizing level, that is, the value of p for which E ( p) = 0. This is because when E ( p) = 0, C p is clearly positive. Property 6 (Default). Very low levels of default may be optimal even when monitoring is quite costly, though it is never optimal to have less default than in the social optimum.
Because this is a completely safe investment, it will earn the safe rate, ρ, on the marginal unit, that is, ρ = H (µ K ). This allows us to write ρ = ρ( K ), ρ < 0. The rest of the available wealth in the economy will be invested in the linear production technology. 1) where λ(ρ) is the optimal leverage ratio from the point of view of borrowers in an economy where the cost of capital is ρ. How about the evolution of wealth in this economy? Given all the assumptions that have already been made, this turns out to be quite straightforward: W t+1 = β[e + H (µ K (W t )) + (W t − µ K (W t )) × (σ E( p(ρ( K ))) − M(ρ( K )))], where p(ρ) is the optimal choice of p when the cost of capital is ρ and M(ρ) is the corresponding level of monitoring per unit of capital.
Because p > p(R, F(K )/K ), it follows that C p can be positive only if the function p E ( p) is a decreasing function of p over a range. This makes it clear that it is entirely possible that C p be negative for all p, implying that implementing high values of p may, paradoxically, require less monitoring than implementing lower values. This is because a high p generates a low R and this improves incentives. In such situations it may be optimal to raise p all the way to its maximum, that is, to p1 .