| Negative | Cause | Prime effect | Then |
| u P | more unemployment | lower wage demands | and thus less inflation |
| P DEF | more inflation | more tax revenue | and thus a lower deficit |
| i YR | a higher rate of interest | makes investments more costly | and thus lower growth |
| YR u | more growth | more demand for labour | lower unemployment |
24. Heterogeneity and nonlinear taxation
Heterogeneity versus homogeneity
Homogeneity assumes that S[p], D[p] and p are real variables, while heterogeneity assumes vectors or densities. This book takes the density approach. In fact, employment e[w] = Min[s[w], d[w] also provides the earnings or income distribution, i.e. the function that gives the number of people earning a level of income w, for labour supply s[w] and labour demand d[w].
Nonlinear versus proportional taxation
The proportional tax is r Y. A linear but non-proportional tax is Bentham[w, x] = r (w - x), though proportionality comes back again by assuming x = 0. A nonlinear tax adds curvature (see chapter 29), and then interacts with heterogeneous labour.
Some literature
The following references put the argument into perspective.
In his presentation of the IS-LM model, John Hicks (1937) could disregard differences in labour as being of secondary complication. For our purposes, however, the case of heterogeneous labour causes a crucial difference. Policy co-ordination then involves three distributions: