Malthus was, broadly, right in his description of the world before 1800. Almost all income was agricultural income, and agricultural income was dependent largely on a fixed factor of production, land. As production technology became better (which happened at a very slow rate), wages increased, lowering death rates and increasing birth rates, which led to growing population. As population increased, less fertile land was brought into production, lowering per capita income. Per capita income fell until the birth-death ratio was again in steady state, with society at a higher level of population than before the new technology, but no richer overall.
This story is only broadly true, however. We do see regions diverge slightly: Europe becomes twice as rich as China by the 1700s, for instance. In a Malthusian world, how is this possible? Voigtlander and Voth propose an interesting new mechanism – their model is much more complicated than what I present here, but the spirit is the same.
Take as given that increased wages led to greater urbanization (people above subsistence have a taste for goods that can only be produced in cities), and that the Malthusian mechanism above holds, returning us to the subsistence steady state after shocks. Europe is rather unique in the following way: higher levels of urbanization there were quite deadly by world standards. Voigtlander and Voth mention three particular reasons why. First, European cities tended to both be filthy and high density. Human waste was often just tossed onto the street in Europe, whereas in China it was much more common to carry the waste to the countryside for use as fertilizer; partly for this reason, China had relatively high rural mortality, and Europe relatively high urban mortality. Second, geography and political circumstances in the early modern era meant that warfare was much more common in Europe than in other parts of the world. Wars of this era generally just meant increased death by disease rather than mass destruction of capital. Third, urban centers traded more, and common disease resistance across regions in Europe was not as prevalent as in China.
Think of this on a standard Malthusian graph. Putting quantity on the vertical axis and income on the horizontal axis, in the steady state equilibrium, the wage is determined by the intersection of a downward sloping death schedule (higher wages=less mortality) and an upward sloping birth schedule (higher wages=more births). A population shock hits: in this case, the Black Death kills an enormous percentage of Europe’s population beginning in the 1300s. Lower population means a temporarily higher wage in the Malthusian mechanism. The higher wage leads to greater urbanization. In Europe, but not in other regions experiencing negative population shocks, the greater urbanization leads to a higher death rate. That is, the death schedule shifts up and to the right. The new steady state intersection of the birth and death schedules that we return to is at a higher income than before the shock. So long-run incomes have increased following a temporary shock, even in the Malthusian world. A nice trick! Note also the counterintuitive nature of the result: Europe prospers in the centuries after the first plague precisely because of its violent, disease-ridden nature. That means you should be careful to interpret the results as explaining why incomes rose, not as arguing for any increase in welfare.
The authors also attempt to show, via a calibration exercise, how relatively important urbanization, disease spread from trade and disease/killing from war are in allowing Europe to grow. These type of exercises are not really for me, but check it out if you are interested – they assign most of the income gains in Europe to the effects of more frequent warfare made possible by taxing urban workers.