RDP 2013-09: Terms of Trade Shocks and Incomplete Information Appendix B: Steady State and Log-linearised Equations

B.1 Steady State

Before deriving the non-stochastic steady state of the model, I normalise the following variables to be in a form that is stationary: , and , where a ^~ denotes a stationary variable. Using these normalisations, the non-stochastic steady state of the model is given by:

where I have replaced the wage rate and the rate of return on capital in the solution to the consumers' problem with the marginal products of labour and capital from the firm's profit maximisation conditions, given by Equations (5) and (6).

B.2 Log-linearised Equilibrium Conditions

To solve the model, I log-linearise the model around its non-stochastic steady state derived in the previous section. The log-linearised equilibrium conditions are:

Production:

Intratemporal optimisation:

Bond market Euler equation:

Capital Euler equation:

Capital accumulation:

Risk-free rate of return:

Current account:

where lower case letters denote a variable's log-deviation from its steady state, that is d_t = lnD_t – lnD^*.