### The Samuelson and Slow Modification

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 ……………………………… (3)
Where,
πe = Expected inflation
u-1 = Degree of demand pressure in labor market

Combining equation 2 and 3 we will get,
π = πe + bu-1 – (1- β) λ ……………………………… (4)

It states that inflation depend upon expected rate of inflation (πe), excess demand pressure in labor market (bu-1) and the term (1 - β) λ. The last term denotes the portion of the growth in labor productivity that is not transformed in money wage.

Thus modifying the Phillips curve, Samuelson and Slow establish the inverse relationship between rate of inflation and unemployment. They recommend the Phillips curve to policy makers as an instrument to formulate the policy program with alternative combination of inflation and unemployment rate because there exists trade off between these variables.

In a conclusion we can conclude the Neo-Keynesian theory of inflation as such that inflation is the consequences of excess demand in labor market or disequilibrium in labor market. Growths in productivity of labor and expected inflation are other explanatory variables of inflation.

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