Fixed Money Wages

Abstract

In the current section, money wages are supposed to be fixed. Apart from this, we shall take the same approach as before. More precisely, w = const will be substituted for the Phillips curve $\dot{w}=\varepsilon w\left( \operatorname{N}\sqrt{\operatorname{N}}-1 \right)$, cf. (7) in section 2. Accordingly, the short—run equilibrium can be described by a system of eight equations:

$$Y=\operatorname{C}+\operatorname{I}$$

(1)

$$C=\left( 1-\beta \delta \mu \right)\operatorname{Y}+\mu K$$

(2)

$$Y={{K}^{\alpha }}{{N}^{\beta }}$$

(3)

$${{K}^{*}}=\alpha Y/r$$

(4)

$$\operatorname{I}=\lambda \left( {{\operatorname{K}}^{*}}=\operatorname{K} \right)$$

(5)

$$\dot{K}=\operatorname{I}$$

(6)

$$w/p=\beta Y/N$$

(7)

$$\operatorname{M}/\operatorname{P}=\operatorname{Y}/{{\operatorname{r}}^{\eta }}$$

(8)

Here α, β, δ, η, λ, μ, w, K and M are given exogenously, while p, r, C, I, K*, $\dot{K}$, N and Y are endogenous variables. It is worth noting that the short—run equilibrium does not depend on labour supply. In addition, the IS—LM equation coincides with that acquired for slow money wages:

$$\frac{\alpha \lambda Y}{\beta \delta \mu Y+\lambda K-\mu K}={{\left\{ \left. \frac{\operatorname{w}{{\operatorname{Y}}^{1/\beta }}\operatorname{K}{{-}^{\alpha /\beta }}}{\beta M} \right\} \right.}^{1/\eta }}$$

(9)