Combining agglomeration economies and endogenous growth without scale effects

ABSTRACT

Increasing returns to scale is essential to both spatial economics and macroeconomic growth. Spatial externalities imply external local increasing returns that generate an uneven spatial distribution of economic activity. While non-rival knowledge also implies increasing returns – in order to endogenise growth – this is not a spatial micro-foundation. Spatial theories of growth must be carefully specified to avoid unintended conclusions about the spatial economy and scale effects. This is demonstrated with a spatial endogenous growth model without scale effects that includes a spatial mechanism that facilitates agglomeration economies for innovation. In this class of models that combine spatial mechanisms with endogenous growth without scale effects, local increasing returns to scale imply that productivity, growth and interest rates are functions of the economy’s spatial distribution, but not its scale.

KEYWORD:

• Endogenous growth
• increasing returns
• agglomeration economies
• scale effects
• spatial macroeconomics

JEL:

• O4
• R1
• R3

ACKNOWLEDGEMENT

For many helpful comments and suggestions, I am grateful to the editor and two anonymous referees.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author.

Notes

1 Throughout this article, the terms ‘increasing returns to scale’ and ‘decreasing returns to scale’ are interchangeable with the terms ‘increasing returns’ or ‘external economies’; and ‘decreasing returns’ or ‘external diseconomies’, respectively. The term ‘returns to scale’ encompasses increasing, constant and decreasing returns to scale. The terms ‘agglomeration economies’ and ‘agglomeration diseconomies’ respectively refer to external increasing and decreasing returns to the scale of cities.

2 There are still increasing and decreasing returns at country scales, such as in government, openness to external trade or from the benefits of internal trade integration, as well as exposure to risk (Damijan et al., 2023), but this is predominantly due to the benefits of trade integration, increasing returns in production and increasing returns for public goods provision, which are all mechanisms that could be included in such models, rather than implicit assumptions about growth. Such mechanisms all generate level effects in productivity, also known as the weak scale effect (Jones, 1999), but there is no strong scale effect in relation to scale and growth.

3 Cost-reducing and quality-improving innovations are equivalent. Quality-improving innovations increase the quantity of final goods produced from intermediates, while cost-reducing innovations increase the quantity of intermediates, and subsequently the quantity of final goods. This means that quality-improving innovations place the technology parameter in the demand function, and cost-reducing innovations place the technology parameter in the intermediate firm’s supply function. Both ultimately reach the consumer’s utility function in the same way. I focus on a cost-reducing innovation example, but the results would also apply to quality-improving innovations.

4 While this condition is not necessary for a large number of local firms or when a firm is infinitesimally small, as in the continuous specification, it is intuitively helpful for the potential situation when the firm operates in isolation since they would experience an observable positive ‘externality’ from their own innovation efforts.

5 The differential with respect to distance assumes that firms do not account for the effect of their own spillovers.

6 While entry peters out such that effort to introduce new varieties is zero in the steady state without population growth, the entry condition is still binding because exit can occur in one location and entry in another. If the model included population growth, entry would occur at a constant rate proportional to the population growth rate but otherwise not affect the conclusions.