Output per capita can rise more quickly that labor productivity if people simply work more hours. They will make more output without doing so in a more productive manner.
Output per capita is measured simply by taking a country’s output (measured by something like gross domestic product) and dividing it by the number of people in the country. By contrast, labor productivity looks at the number of hours that people work. It takes the country’s output and divides it not by the number of people in the country but by the number of hours worked by the people in the country.
Looking at these definitions, we can see how output per capita can grow faster than labor productivity. Let us imagine that people in a country simply start to work more hours or that more people in the country enter the labor force. In either case, the country will produce more output per person. However, the country will not really be more productive since the output for every hour worked has not gone up. Labor productivity will only rise if people start to work more efficiently or if they get technology that allows them to make more per hour.
Output per capita can rise, then, simply with effort. By contrast, labor productivity must rise through greater efficiency. This is why output per capita can rise even if labor productivity does not.