# Unemployment, Recession and Effective Demand

## The Contributions of Marx, Keynes and Kalecki

## Claudio Sardoni

# Appendix B: Effects of Wage Changes in Keynes’s Model

## Claudio Sardoni

## Extract

Proposition 1 At p = p* and r = r*, it is ∂p/∂r > 0 From (5.14), let us consider the implicit function K(c, p, r, w) ≡ F (p, w) – M(c, p, r, w) = 0 From (5.8) and (5.11), and remembering that in equilibrium p = pe, M(c, p, r, w) can be also written as M(c, p, r, w) = cF (p, w) + cG(r, p, w, i, E) with G(r, p, w, i, E) = rI/p. Since it is ∂G/∂p < 0 and ∂G/∂r > 0, then ∂p∂r = – (∂K/∂r)/(∂K/∂p) = – [s(∂F/∂r) – c(∂G/∂r)]/[s(∂F/∂p) – c(∂G/∂p)] with s = (1 – c). Since it is ∂F/∂r = 0, ∂G/∂r > 0, [s(∂F/∂r) – c(∂G/∂r) > 0, [s(∂F/∂p) – c(∂G/∂p)] > 0, then ∂p/∂r > 0 Proposition 2 At p = p* and r = r*, it is (B.1) ∂r/∂w > 0 ∂p/∂w > 0 The sign of ∂r/∂w can be easily determined from (5.15). Let us consider the implicit function 154 Effects of wage changes in Keynes’s model 155 R(r, w, i, E) ≡ G(r, w) – H(r, i, E) = 0 It is ∂r/∂w = – (∂R/∂w)/(∂R/∂r) = – [(∂G/∂w) – (∂H/∂w)]/[(∂G/∂r) – (∂H/∂r)] = (∂G/∂w)/[(∂G/∂r) – (∂H/∂r)] as ∂H/∂w = 0. Since it is ∂G/∂w < 0, ∂G/∂r > 0 and ∂H/∂r < 0, ∂r/∂w > 0 (B.2) The sign of ∂p/∂w is immediately...

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