A fixed budget must be allocated to a finite number of different projects with uncertain outputs. The expected marginal productivity of capital in a project first increases then decreases with the amount of capital invested. Such behavior is common when output is a probability (of escaping...

We examine the investment decision problem of a group whose members have heterogeneous time preferences. In particular, they have different discount factors for utility, possibly not exponential. We characterize the properties of efficient allocations of resources and of shadow prices that would...

We examine the investment decision problem of a group whose members have heterogeneous time preferences. In particular, they have different discount factors for utility, possibly not exponential. We characterize the properties of efficient allocations of resources and of shadow prices that would...