Discrete dynamics in a two-country model with a durable good

Abstract

In this paper, we extend Doi et al. (2007) in the sense that households in both countries consume a durable good. Although this generalization makes the model much complicate, it will be shown that under the standard Cobb–Douglas preferences, the model has a unique steady state and saddle-point stability.

Keywords::

• stability
• dynamical systems
• optimization
• economics
• saddle point

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

^1. We assume that one unit of computer generates one unit of service flow during each period. So, $B_t$ also denotes the stock of computers.

^2. Here, we assume labour coefficients satisfy the following inequality $a_1/a_2<p<{\displaystyle a_1^{*}}/{\displaystyle a_2^{*}}$.

^3. Notice that from (20) to (22), we have $\delta B+{\delta B}^{*}=Y^{*},$ and that this implies market clearing of the durable good in the steady state.