continuous investment and decreasing returns to scale). Consider the continuousinvestment model, with one modification: investment I yields return R(I) in the case of success, and 0 in the case of failure, where R > 0, R < 0, R (0) > 1/pH, R (∞) ∗ denote the level of investment that maximizes total surplus: pHR (I∗) = 1.
(i) How does investment I(A) vary with assets?
(ii) How does the shadow value v of assets (the derivative of the borrower's gross utility with respect to assets) vary with the level of assets?