Fixed Money Wages

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: 1$$Y=\operatorname{C}+\operatorname{I}$$2$$C=\left( 1-\beta \delta \mu \right)\operatorname{Y}+\mu K$$3$$Y={{K}^{\alpha }}{{N}^{\beta }}$$4$${{K}^{*}}=\alpha Y/r$$5$$\operatorname{I}=\lambda \left( {{\operatorname{K}}^{*}}=\operatorname{K} \right)$$6$$\dot{K}=\operatorname{I}$$7$$w/p=\beta Y/N$$8$$\operatorname{M}/\operatorname{P}=\operatorname{Y}/{{\operatorname{r}}^{\eta }}$$ 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: 9$$\frac{\alpha \lambda Y}{\beta \delta \mu Y+\lambda K-\mu K}={{\left\{ \left. \frac{\operatorname{w}{{\operatorname{Y}}^{1/\beta }}\operatorname{K}{{-}^{\alpha /\beta }}}{\beta M} \right\} \right.}^{1/\eta }}$$