Evenwicht: een Numerieke Verificatiebenadering

The equilibrium for a simple and closed economy with consumption and planned investment, like that which was determined graphically in the previous video, can also be determined mathematically.

In this example, the consumption function is defined as consumption equals one hundred plus zero point seven five times income. Planned investment remains fixed at twenty-five dollars.

Begin by evaluating an income level of four hundred dollars. Substituting this value into the consumption function yields four hundred. Adding investment results in total planned expenditure of four hundred and twenty-five dollars. Since planned spending at this level of income exceeds output, this leads to an unplanned reduction in inventories. The economy is not in equilibrium.

Next, evaluate income at 500 dollars. At this level of income, planned expenditure equals output, confirming this as the equilibrium level of income

Finally, at six hundred dollars, planned spending falls short of output, resulting in unplanned inventory accumulation.

Thus, only at five hundred dollars does planned expenditure equal output, indicating equilibrium income.