autonomous and induced investment; the accelerator

Imagine a big circle where money keeps moving around. 👇 Households (🏠) give labour to Firms (🏭) and receive wages (💰). Firms use those wages to buy goods and services from households and pay profits back to them. The circle continues with the Government (🏛️) collecting taxes and spending on public goods, and the Foreign Sector (🌍) buying and selling with the rest of the world. Every arrow in this circle is a flow of money or goods – the circular flow of income.

Autonomous Investment (🔧) is the part of investment that happens regardless of current income levels. Think of it as a new gadget that a company buys because it’s the latest tech, not because people are buying more stuff right now.

Induced Investment (📈) rises when households earn more money and want to spend more on new things, like a family buying a bigger house when their salaries increase.

Formula: $I = I_a + I_i$ where $I_a$ = autonomous and $I_i$ = induced.

The accelerator says that investment is driven by the change in output (ΔY), not just the level of output.

Analogy: Imagine a factory that builds cars. If the demand for cars suddenly jumps, the factory ramps up production quickly – it “accelerates” to meet the new demand.

Mathematical form: $$I = a + b\,\Delta Y$$ where:

• $a$ = autonomous investment (fixed)
• $b$ = accelerator coefficient (how much investment changes for each unit change in output)
• $\Delta Y$ = change in national income/output