Overview¶
In the previous section we distinguished workers by their skills, but we did not model what they do. We also took capital as an aggregate input for production, while not specifying how it is actually used in the workplace. In practice, the type of technology we covered made one type of labor more productive in every activity, and the production function determined how easily that labor could replace another input. We now open up this production function. Our objective is to describe the activities needed for production and then determine who performs them. We call these activities tasks.
This gives us another way to think about substitution. A firm can respond to a higher wage by using less of the tasks performed by the workers whose wage has increased. But it can also assign some of those same tasks to other workers or to machines. The task-based model lets us distinguish these two responses.
So, who (or what) should perform each task? Part of the answer lies in who is the most productive at performing the task, but productivity alone cannot give us the answer. Not because a robot is better than person at doing something we should immediately automate (assign the task to the robot). Whether we assign the task to the person or the robot is also influenced by relative cost (we are back to \(w/r\)!). It turns out, Economists have long studied this type of scenario. The most famous case is that of international trade and is the origin the of the principle of comparative advantage developed by David Ricardo in the 1800s.
The Ricardian model of trade is still used to understand how production is organized across countries. Modern models of trade are evolutions of the basic framework in Dornbusch et al. (1977). Labor economists have adapted the assignment problem of Ricardian trade to the problem of tasks. In the task model, skill groups (including machines) take the place of countries and tasks take the place of goods: each task goes to the group with the lowest unit cost. Differences in relative productivity across tasks and equilibrium wages jointly determine the assignment boundaries.