
240 An Economic History of the
English Poor
Law
utility large enough to keep them from leaving the firm.
11
The model is
outlined and the conditions under which the manufacturer will choose to
lay off workers are given in footnote 12.
12
There it is shown that layoffs
will occur during a cyclical downturn if the output of the marginal
worker (which is affected by the level of demand) is less than the cost to
the manufacturer of employing him minus the amount the worker is
willing to pay to avoid layoffs. The number of layoffs is determined by
the extent of the downturn and by the size of the contribution of taxpay-
ers other than manufacturers to the poor rate (the poor relief subsidy).
The worse the state of the economy, the lower the marginal product of
labor for any given-sized labor force, and hence the more layoffs that
occur. Similarly, the larger the poor relief subsidy, the lower the cost to
an employer of laying off workers and therefore the more layoffs that
will occur in any given downturn.
The result just described corresponds to the situation in which work-
ers had to be unemployed to collect
relief.
In many cities factory work-
11
Huberman (1987: 179) writes that "in urban Lancashire spinners had the opportunity of
moving quite readily from factory to factory, and to reduce turnover firms had to meet
workers' demands."
12
The model is essentially the same as the model developed in Chapter 3. I therefore will
only sketch the manufacturer's problem. The manufacturer's production function is y =
g(€, x), where € is labor input and x is a random variable denoting the state of the
economy. I assume that g
u
> 0 and g
x
> 0, that is, high values of x signify boom periods
and low values of x signify recessions. Note that the only difference between the manufac-
turer's production function and the farmer's production function in Chapter 3 is the
interpretation of the random variable x. Workers' utility is defined exactly as in Chapter
3.
The manufacturer's objective is to maximize profits subject to the constraint that the
expected utility of the contract offered workers must be at least as large as their reserva-
tion utility V*.
The method used to solve the manufacturer's problem is detailed in the Appendix to
Chapter 3. The conditions under which layoffs occur are obtained from the first-order
conditions of the Lagrangian. The manufacturer will choose to lay off workers in year t
if, for some number of workers n
t
(x
t
) < N
8i[n
t
(x
t
)h
t
(x
(
), x]h
t
{x) < c
t
(x
t
) - d
t
(x
t
) + s - z
t
(x
t
)
where n(x) is the number of workers employed in state x, N is the total number of
workers under contract, h is the hours per worker, c is the consumption of an employed
worker, d is the consumption of an unemployed worker, s is the contribution of taxpay-
ers other than manufacturers to the poor rate (the poor relief subsidy), and z is the
marginal benefit of being employed rather than unemployed. The above inequality says
that the manufacturer should lay off workers if the output from the marginal worker,
given x
n
is less than the cost of employing him (c, - d
t
+ s) minus the amount the worker
would be willing to pay not to be laid off, z
r
For any given value of s > s*, the lower the
value of x
t
(that is, the worse the state of the economy), the more layoffs that will occur.
Also,
for any given state of the economy, the larger the poor relief subsidy, the lower the
cost to manufacturers of laying off workers. For any value of x, there exists a critical
value of 5, 5*, so that if s > s*, manufacturers will choose to lay off workers. Given s is
greater than s*, the larger the value of 5, the more layoffs that will occur.