Monopsony - Dynamic Problems

Dynamic Problems

In many real-world situations a monopsonist firm will have to maximise its profits through time, rather than instantaneously as in the previous static model. In all such cases, any short-run outcomes will have to be balanced against longer-run ones, and the resulting equilibrium may differ.

The simplest dynamic model to bring out this idea, used in Boal and Ransom (1997), is one where the supply of labour to the firm reacts to wage changes with a lag, due for instance to information costs and search behaviour. Assume hence that the supply function has a distributed-lag specification, leading to:

,

where the subscript refers to the time period and is increasing in both arguments. Inverting this function gives:

,

with

.

If the firm has a time-discount rate, the present value of profits is now given by:

.

The first-order condition to maximise this present value is:

.

Define next the short-run simultaneous and lagged inverse supply elasticities respectively as:

.

Now, assume these elasticities to be constant over time. Assume further a steady state, with and . Then the first-order condition gives the exploitation rate as:

.

Finally, the steady-state long-run inverse elasticity, is given by the sum of the two short-run inverse elasticities defined above, and so one has:

.

The exploitation rate is thus a weighted average of the short- and long-run inverse supply elasticities, where the weight of the long-run one is much bigger, because is much smaller than unity even when the discounting period is one year. It follows that, as the long-run (direct) supply elasticity of labour tends to be much higher than the short-run one, this very simple dynamic model predicts an exploitation rate which is much smaller than the one produced by static analysis.

However, less simplified dynamic models tell less simple stories. Even the employment effect of minimum wages is not as clear cut as static models would have.