A new route to the rapid growth of the service sector: rise of the standard of living

In the present study, we set up a continuous-time two-sector optimal growth model with services and manufacturing goods and then examine structural change: the rapid growth of the service sector. Earlier studies of structural changes can be separated into two categories: preference-driven and technology-driven. Here we introduce a new and distinct category of structural change: consumption externality identified as rise of the living standard. A key assumption is that (1) a representative consumer has a non-homothetic Stone–Geary type utility function with respect to manufacturing goods and that (2) its subsistence level will be regarded as the standard of living and will be affected by the average consumption of manufacturing goods, which also affects the consumption level of services. We also assume that the manufacturing sector is more capital-intensive than the service sector, which takes an important role in our proofs. Results show that a steady state equilibrium exists that is globally stable as well as saddle-point stable. Then, given certain production parameters in a steady state, there exists optimal steady state where the value-added and employment shares by service sector will dominate those of the manufacturing sector under the condition that external effects of the service sector dominates capital-intensity effect of the manufacturing sector. In other words, through the transition process, the service sector will dominate the manufacturing sector in the steady state.