A macroeconomic problem involves calculating equilibrium income given consumption, investment, government spending, and tax functions.

Here's a breakdown of the problem:

Given Information:

• Current level of income ($Y_{current}$) = 3,000 billion FCFA (This is assumed to be the full employment income, $Y_{FE}$)
• Marginal Propensity to Consume ($c$) = 0.8
• Autonomous consumption ($C_0$) = 100 billion FCFA
• Investment ($I$) = 300 billion FCFA
• Government spending ($G$) = 200 billion FCFA
• Direct taxes ($T$) = $0.1Y$ (Tax rate $t = 0.1$)

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a) Calculate the equilibrium level of national income.

The equilibrium condition for national income is given by:

$$Y = C + I + G$$

Where consumption $C$ is given by $C = C_0 + cY_d$, and disposable income $Y_d = Y - T$.
Since $T = tY$, we have $Y_d = Y - tY = Y(1-t)$.
Substituting $Y_d$ into the consumption function:

$$C = C_0 + cY(1-t)$$

Now, substitute $C$ back into the equilibrium equation: