The Black Death: (a) Wages were higher after the Black Death because of diminishing returns. Our production model exhibits diminishing returns to labor: each additional unit of labor increases output by less and less. So if the amount of labor is reduced, the marginal product of labor — and hence the wage — increases. The reason is that capital stays the same: each remaining worker is able to work with more machines, so his productivity rises. In fourteenth-century Europe, the marginal workers could move to better land and discard old broken-down tools. Graphically, this can be seen by considering the supply-and-demand diagram for labor in Figure 4.2(b). If the supply of labor shifts back (because a large number of workers die), the equilibrium wage rate increases. Draw this graph — including the shift in the labor supply curve — to see the result for yourself. Mathematically, the result can be seen in the solution for the wage rate in our production model, shown in Table 4.2 and reproduced here: Holding capital constant, a decrease in labor L will increase the wage. It is important to notice that Y * is an endogenous variable in the equation above. So we can’t use the first part of the equation to answer this question, because Y * itself changes when there is a decrease in labor. (b) The European population fell by one-third, so two-thirds of the population remained: fell to 2/3. Plugging the quantity into the wage equation above shows that the wage would be expected to increase by a factor of (3/2)1/3 1.14, or by about 14%.
The Black Death:
(a) Wages were higher after the Black Death because of diminishing returns. Our production model exhibits diminishing returns to labor: each additional unit of labor increases output by less and less. So if the amount of labor is reduced, the marginal product of labor — and hence the wage — increases. The reason is that capital stays the same: each remaining worker is able to work with more machines, so his productivity rises. In fourteenth-century Europe, the marginal workers could move to better land and discard old broken-down tools. Graphically, this can be seen by considering the supply-and-demand diagram for labor in Figure 4.2(b). If the supply of labor shifts back (because a large number of workers die), the equilibrium wage rate increases. Draw this graph — including the shift in the labor supply curve — to see the result for yourself. Mathematically, the result can be seen in the solution for the wage rate in our production model, shown in Table 4.2 and reproduced here:
Holding capital constant, a decrease in labor L will increase the wage. It is important to notice that Y * is an endogenous variable in the equation above. So we can’t use the first part of the equation to answer this question, because Y * itself changes when there is a decrease in labor.
(b) The European population fell by one-third, so two-thirds of the population remained: 
fell to 2/3. Plugging the quantity into the wage equation above shows that the wage would be expected to increase by a factor of (3/2)1/3 
1.14, or by about 14%.
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