dLog[P] = dLog[P]* - 0.1 Log[ u / u* ]
would give an expectations augmented form, and when u = u* then expectations will be fulfilled, and LE = LS (1 - u*).
It is useful to note that above model does not yet contain an explicit reaction function of the monetary authorities with regarding to inflation. Money can be fixed or chosen to grow at a predetermined rate. In practice there will be a flexible reaction, and then part of the ‘Phillipscurve regression between dLog[P] and u’ will reflect that reaction function.
Macro-economic interactions
The textbook relations are simple in themselves, but the interactions already can be rather complicated. Figure 18 presents some common macro-economic interactions.
Figure 18: Some macro-economic interactions
The influence of income in that figure is stated in terms of growth dLog[YR], [76] and the influence of prices is stated in terms of inflation dLog[P]. Positive transmissions are in black and explained in Table 5, negative transmissions are dashed in red and explained in Table 6.
| Positive | Cause | Prime effect | Then | Then again |
| YR P | growth | increases demand | adds to inflation | |
| u DEF | more unemployment | less income, less tax revenue | more expenditure on benefits | higher deficit |
| P i | more inflation | the Central Bank (CB) raises interest rates to fight it | possibly, though, inflation means more profits and a reduced demand on loans | and thus a lower rate of interest: but then the CB will maintain the level of interest |
| i DEF | higher interest rates | the government has a higher interest bill | higher deficit | |
| DEF i | a higher deficit | more demand for loans, more supply of bonds | thus a higher rate of interest | |
| DEF YR | a higher deficit | sustained expenditure | and thus sustained growth (at least by that channel) |