How is the equilibrium level of income and output determined in a four-sector model? Explain using both the aggregate demand-aggregate supply and the leakages equals injections approach.

The aggregate demand (AD) is the sum of the demand from households, firms, government, and the foreign sector (net exports). Mathematically, it can be represented as: AD = C + I + G + (X - M) where C is consumption, I is investment, G is government spending, X is exports, and M is imports. Aggregate supply (AS) represents the total output produced by the economy at a given price level. In the four-sector model, the equilibrium level of income and output occurs when aggregate demand equals aggregate supply (AD = AS). In other words, the total demand for goods and services equals the total supplied output at a particular price level. In equilibrium, there is no tendency for the economy to expand or contract, and output remains stable.

In this approach, we focus on the flow of income between sectors in the economy. The total income generated in the economy can either be spent or leaked out of the circular flow. In the four-sector model, leakages include savings (S), taxes (T), and imports (M). Injections include investment (I), government spending (G), and exports (X). The equilibrium level of income and output is achieved when total leakages equal total injections. Mathematically, it can be represented as: S + T + M = I + G + X When leakages equal injections, it means that all the income generated in the economy is either spent on goods and services or returned back into the economy as investment, government spending, and exports. In this situation, there is no tendency for the economy to expand or contract, and the output remains stable.

Both approaches, AD-AS and leakages equals injections, lead to the same conclusion regarding the equilibrium level of income and output in the four-sector model. In the AD-AS approach, equilibrium is achieved when AD = AS, and in the leakages equals injections approach, equilibrium is achieved when S + T + M = I + G + X. Although these are two different ways of representing equilibrium in the economy, they are essentially two sides of the same coin. Both convey the idea that the equilibrium level of income and output occurs when all factors contributing to economic activity are balanced, ensuring stability within the four-sector model.