The Black Death. In Section 8.2.1 we discussed how a major drop in the size of the population could actually raise living standards. Consider an economy that is described by the model in that section and is currently at the steady state level of population L*.

(a) There is a one-time drop in population, to L0 6 L*, following an outbreak of the plague. Draw a graph showing the path of income per capita, y, in this economy over time. Include on the graph the time period prior to the plague, the plague itself, and the time period following the plague as the economy recovers back to steady state.

(b) An alternative way to think of a plague is as a drop in the productivity of the population. Start over with an economy at the steady-state level of population L*. Now let there be a permanent drop in productivity, B, due to the plague. Draw a new graph showing the path of income per capita, y, in this economy over time. Again include the period prior to the productivity drop, the drop itself, and the time period following as the economy goes to its steady state. How does income per capita compare in this situation to the one in (a)?

(c) Finally, start over again with the economy at steady state with L* in population. Now let there be a temporary drop in productivity, B, due to the plague. That is, B falls for several years, and then goes back to its original level. Draw a new graph showing how income per capita evolves over time, similar to the prior parts in this question. How does income per capita compare in this situation to that in

(a) and (b)?