Utilitarianism, prioritarianism, and intergenerational equity: A cake eating model

We use a simple consumption model, the so-called cake eating model, to study the interaction of equity, time and risk in social decision making. Total consumption, the “cake”, is uncertain. The social planner allocates consumption between two agents (representing two generations), by assigning the first a determinate amount, with the second receiving the risky remainder. We study this consumption allocation decision using three social welfare functions: utilitarianism, ex ante prioritarianism, and ex post prioritarianism. Under standard assumptions, ex ante prioritarianism allocates more consumption to the first generation than utilitarianism. Thus, a concern for equity, in the ex ante prioritarian sense, means less concern for the risky future. By contrast, ex post prioritarianism normally chooses less consumption for the first generation than utilitarianism. We discuss the robustness of these optimal consumption allocations to learning and to more complicated social welfare functions.