next up previous
Next: The bargain Up: Regional unemployment insurance Previous: Introduction

Assumptions and bargaining setup

In order to keep the analysis manageable, we employ the following assumptions and standardisations:
A1
A federal state consists of two regions ($i \in 1,2$) which differ only with respect to the endowment of an immobile, inelastically supplied factor of production subsequently referred to as infrastructure, $x^i$, with $x^1>x^2$, i.e. region 1 is the rich region and region 2 is poor.
A2
In each region, many ($K$) identical firms produce a single homogeneous good which is taken as numeraire. The technology of a representative firm shall be described by the production function

\begin{displaymath}
f^i=f(n^i,x^i),
\end{displaymath}

where $n$ denotes labour input. Labour supply per worker is standardised to unity, so that $n$ symbolises the number of employed workers as well. Denoting derivatives with subscripts, it is assumed that $f_{n^i}>0$, $f_{x^i}>0$, $f_{n^in^i}<0$. Additionally, the cross-derivative is assumed to be positive, $f_{n^ix^i}>0$, meaning that infrastructure enhances the productivity of labour. Infrastructure is costless, and there are no fixed costs, so that profits of a firm can be written as $\pi^i=f(n^i,x^i)-n^i w^i$, where $w$ signifies the gross wage rate per worker. Profit maximisation yields the inverse labour demand function:
\begin{displaymath}
f_{n^i}=w
\end{displaymath} (1)

A3
$M$ identical workers have the same concave utility function:

\begin{displaymath}u^i=u(c^{i,j}),\end{displaymath}

where $c$ stands for consumption of the homogenous good3, and where the superscript $j$ with $j \in e,u$, indicates the occupational status of a worker. If $j=e$ (employed), consumption reads $c^{i,e}=(1-\tau^i)w^i$, where $\tau$ is the proportional UI tax rate. In the case $j=u$ (unemployed), consumption reads $c^{i,u}=\beta^i \overline{w^i}$. The variable $\overline{w}$ denotes the wage level used to calculate UI benefits, and $\beta$ is the benefit rate. Workers maximise expected utility by choosing the region where they supply labour.
A4
Ex ante, half of the workers live in each region. We assume that migration takes place in one direction only, namely, from the poor to the rich region. If a worker migrates, costs corresponding with an annuity of $k$ occur. In both regions, workers are distributed equally over the firms, sharing the same employment opportunities within the region (Creedy and McDonald; 1991, p. 348). The number of workers per firm is denoted by $m$.
A5
All workers attached to a firm are members of a trade union. Each firm bargains with a trade union over the gross wage rate $w$ payed to all employed workers, while the firms retain control over employment. Unions maximise the expected utility of a representative member (see e.g. Oswald; 1985, p. 163). We employ the symmetric Nash solution to the bargaining problem, which maximises the geometric mean of a unionīs and a firmīs payoff. Firms attain zero profits if the bargain breaks down, so that the payoff of an agreement equals the profits (Creedy and McDonald; 1991, p. 350). The `threat point' of a union is given by the situation when all of its members receive UI benefits. The payoff of a union is thus the difference between the expected utility of a representative worker in the case of an agreement, and the utility of an unemployed worker (see Farber; 1986, p. 1070).
A6
The UI is obliged to balance its budget. The exact form of the budget constraint depends on whether $\beta$ or $\tau$ is used to attain an equilibrated budget (while the other parameter is given exogenously), and whether the UI is central or regional. The following cases are being considered:
Model TC.
The tax rate is adjusted to adapt the revenues of the UI to its expenditures, while the benefit rate is exogenous. Both, tax rate, and benefit rate are uniform across the regions.
Model TR.
Like in model TC, the endogenously determined parameter is the tax rate of UI. The UI has to equilibrate its budget within each region seperately, so that, in general, the tax rate differs between the regions, while the benefit rate remains uniform.
Model BC.
The benefit rate is used to equilibrate the budget for a given tax rate. Both are uniform across the federal state.
Model BR.
As in model BC, the benefit rate is choice variable, but with regionally balanced budgets, which leads to differences of the benefit rates, whereas the tax rate is uniform.
Because firms and unions take benefit and tax rate, as well as the number of attached workers as given, the wage-bargain can be considered in a seperate submodel. The results of the subsequent analysis thus apply to each of the models.

Subsections
next up previous
Next: The bargain Up: Regional unemployment insurance Previous: Introduction
Helge Sanner: Regional Unemployment Insurance, Potsdam 2001