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What are the conditions for equilibrium of two-sector economy?

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In a two-sector economy, equilibrium occurs when aggregate demand equals aggregate supply, saving equals investment, and there are no unintended changes in inventories.
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Solution and Explanation

In a two-sector economy, there are two main sectors: households and firms. The equilibrium of a two-sector economy is achieved when the total income generated by the economy is equal to the total expenditure. The conditions for equilibrium in a two-sector economy are as follows:

Step 1: Aggregate Demand Equals Aggregate Supply.
The total aggregate demand (AD), which is the sum of consumption (C) and investment (I), must equal the aggregate supply (AS), which is the total income (Y). Thus, the equilibrium condition is: \[ AD = AS \quad \text{or} \quad C + I = Y \] This implies that the total amount spent in the economy (consumption and investment) must be equal to the total output (income).

Step 2: Saving Equals Investment.
At equilibrium, saving must be equal to investment. Saving (S) is the portion of income that is not consumed, while investment (I) refers to the expenditure on new capital goods by firms. The equilibrium condition can be expressed as: \[ S = I \] This means that the total amount saved in the economy must be equal to the amount invested by firms.

Step 3: No Unintended Inventory Changes.
In a two-sector economy, firms produce goods and services and expect them to be sold. If firms produce more than what is demanded (i.e., if aggregate demand exceeds aggregate supply), there will be an unintended increase in inventory. This is unsustainable and will lead to a reduction in production. Conversely, if demand exceeds supply, firms will reduce inventories and increase production. Equilibrium occurs when there are no unintended changes in inventories, meaning production is exactly equal to demand.
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