Consumption, investment, multiplier, accelerator

Households split income between consuming and saving, and the consumption function C = a + bY says consumption has an autonomous part (a) and an income-driven part (bY, where b is the marginal propensity to consume). Investment is more volatile: firms invest when the expected return beats the interest rate, and the accelerator says investment responds to changes in output, not just its level. Worked example: with MPC 0.8, the multiplier is 1/(1 - 0.8) = 5, so a 100 rise in investment raises income by 500; and with a capital-output ratio of 2, a 100 rise in output induces 200 of investment through the accelerator.