In the 14th century, Europe experienced a devastating epidemic of bubonic plague. This epidemic was called the Black Death. About a third to half of the whole population in Europe died. This problem studies how the Black Death affected the well-being of those who were lucky to survive the plague.In Europe of that time, labor L and land X were main factors of production. Both labor and land were in fixed supply: everybody capable of working would work in the field. Suppose the supply of labor is equal to L¯ and the supply of land is equal to X¯. The production function takes the form Y = L^(1/2)X^(1/2).
(A) Obtain the equations for the demand for labor and the demand for land.
(B) How do the equilibrium employment, real wage, real rental rate, and output change in responseto the Black Death? Show these changes on two diagrams: the labor market and the land market.1
(C) Let’s look at workers and land owners. How does the Black Death affect income inequality: who loses from the epidemic? Who gains?
(D) (Harder!) Consider the production function in general form Y = LαXβ. Let the reductionin population be 50%. Suppose, on average, wages rose by 90%. What value of α would beconsistent with these observations? Write out an equation you would need to solve to find α