Final answer:
In the Keynesian-cross analysis, the equilibrium level of national income can be determined by setting total planned spending equal to national income. By substituting the given values into the consumption function and solving for Y, we find that the equilibrium level of national income is approximately 166.67.
Step-by-step explanation:
In the Keynesian-cross analysis, the equilibrium level of national income (Y) can be determined by setting total planned spending (Aggregate Expenditure or AE) equal to national income.
The consumption function is given by C = 20 + 0.7(Y - T), where C represents consumption, Y represents national income, and T represents taxes.
Planned investment is given as 100, government spending (G) is 100, and taxes (T) is 100. By substituting these values into the consumption function, we get C = 20 + 0.7(Y - 100).
We can then calculate AE by adding C and G, which gives us AE = C + G = 20 + 0.7(Y - 100) + 100.
At equilibrium, AE is equal to Y, so we can write the equation as Y = AE = 20 + 0.7(Y - 100) + 100. Solving for Y:
Y = 20 + 0.7(Y - 100) + 100
Y = 20 + 0.7Y - 70 + 100
0.3Y = 50
Y = 50 / 0.3
Y ≈ 166.67
Therefore, the equilibrium level of national income (Y) is approximately 166.67.