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The Samuelson and Slow Modification

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The Samuelson and Slow Modification
Samuelson and Slow (1960) modified the Phillips curve so that it represents the relationship between rate of inflation and rate of unemployment. The link between wage inflation and price inflation was established through markup equation which may be stated as below:  P = (1 + a) WN/Y ……………… (1) Where, P = general level of price      W = money wage rate      N = number of employment      Y = real output      a = constant profit margin
In this above equation WN/Y denotes the unit labor cost – the cost of labor per unit of output. Using the concept of labor productivity (p = Y/N) equation (1) can be written as,      P = (1 + a) W/p
Differentiating the equation after natural log transformation we will get,      π = gw – λ ……………….. (2)
Here, inflation rate (π) is equal to difference between rate of growth in money wage rate (gw) and the rate of growth in labor productivity (λ).
Further, let us assume that Phillips curve is of the following form.  gw = πe + bu-1 + βλ…