IS-LM and AD-AS Diagrams

At first we shall establish the pertinent IS-LM diagram. Substitute (2), (4) and (5) into (1) from section 2, respectively, and solve for r to get the equation of the IS curve: 1$$r = \frac{{\alpha \lambda Y}}{{\beta \delta \mu Y + \lambda K - \mu K}}$$ If λ<μ, an increase in Y causes a reduction in r, which empirically seems to be sound. Conversely, if λ>μ,an increase in Y brings about an increase in r. Henceforth, it will be assumed throughout that: 2$$\lambda < \mu $$Accordingly, the IS curve is downward sloping, see figure 1. Over and above that, r rises as K goes up, so the IS curve shifts to the right. How is income affected by capital formation? Obviously, two counteracting forces are at work. On the one hand, capital accumulation means wealth accumulation. Therefore households save less and consume more, thus stimulating aggregate demand and output. On the other hand, the higher the stock of capital, the less firms do invest, thereby curbing aggregate demand and output. Under the premise λ< μ, the first channel appears to be stronger.