A Theory of Spatial Allocation of Leisure Time : In-home or Out-of-home?

The impact of time allocation on the economy and society has spatial characteristics, especially spatial allocation of leisure time (SALT). To explain the decision-making mechanism of SALT, we divide time from the perspective of space and construct the individual utility function to transform SALT problem into a dynamic optimization process of in-home leisure time (ILT) allocation. Based on the solution of the equilibrium, we analyze the numerical characteristics of the average ILT (AILT) when the entire society achieves the equilibrium. In our model, there is a threshold and AILT is only determined by this threshold. And the variance of ILT is only affected by the individual's collectivism tendency of ILT (CTILT). We claim that if AILT threshold remains the same, the only approach to change AILT is that individuals change their own allocation by the strong hand. Via simulation and analysis, our theory of SALT can explain the spatial distribution characteristics of population in reality