IS-LM and AD-AS Diagrams

In the current section, we shall inaugurate the pertinent IS-LM and AD-AS diagrams. Let us start with the IS curve. Substitute (13), (15) and (16) from section 2 into (12) and solve for r: 1$$r=\frac{\alpha \lambda y}{sy+\left( \lambda -n \right)k}$$ This is the IS equation. If λ ≶ n, then dr/dy ≶ 0. In order to obtain a downward sloping IS curve, we posit 2$$\lambda <n,$$ see figure 1. And an increase in k causes an increase in r, so the IS curve goes to the right. Put another way, a rise in capital per head leads to a rise in income per head. Obviously two counteracting forces are at work. On the one hand, a rise in capital per head lifts that level of investment per head which is required to keep up capital per head. This in turn raises aggregate demand and income, in per capita terms, respectively. On the other hand, according to the flexible accelerator λ(k* − k), the rise in capital per head lowers investment, aggregate demand and income, again in per capita terms. Granted λ < n, the first channel of transmission will dominate.