Optimal equity split under unobservable investments

This paper examines optimal equity split between a penniless entrepreneur (E) and a deep-pocketed venture capitalist (V) with a two-stage investment in a project under unobservable project inputs. The first-stage investment explores project profitability, and the final success probability is a Cobb-Douglas production function form of V's unobservable investment scale, E's and V's private effort. We show that if project profitability is good enough, optimal equity split and the welfare loss rate arising from moral hazard are explicitly determined by inputs' output elasticities, independent of project profitability and inputs' costs. If project profitability is not contractible, we propose a new renegotiation mechanism. The renegotiation is necessary only when V's participation constraint is not met after project profitability is revealed. We specify the thresholds determining whether E should abandon the project, whether E should go ahead without any changes, and whether E should increase V's equity or roll back cash to V. We show that the initial wealth transferred from V to E can be exploited during the renegotiation to realize a significant Pareto improvement