1. **Problem statement:** We have the economic model equations: $$Y = C + I_0 + G_0$$ $$C = A + b(Y - Y_0)$$ $$G_0 = gY$$ We need to find: - The number of endogenous variables. - The economic meaning of parameter $g$. - The equilibrium level of income $Y^*$. - The restriction on parameters for a solution to exist. 2. **Identify endogenous variables:** Endogenous variables are those determined within the model. Here, $Y$ (income) and $C$ (consumption) depend on each other and parameters. $I_0$ and $Y_0$ are exogenous constants. $G_0$ depends on $Y$ via $gY$. So the endogenous variables are $Y$ and $C$. 3. **Economic meaning of $g$:** The parameter $g$ represents the marginal propensity of government spending relative to income. It shows how government spending $G_0$ changes with income $Y$. A higher $g$ means government spending increases more as income rises. 4. **Find equilibrium income $Y^*$:** Substitute $C$ and $G_0$ into the income identity: $$Y = (A + b(Y - Y_0)) + I_0 + gY$$ Simplify: $$Y = A + bY - bY_0 + I_0 + gY$$ Group terms with $Y$: $$Y - bY - gY = A - bY_0 + I_0$$ $$Y(1 - b - g) = A - bY_0 + I_0$$ Solve for $Y^*$: $$Y^* = \frac{A - bY_0 + I_0}{1 - b - g}$$ 5. **Restriction for solution existence:** The denominator must not be zero to avoid division by zero: $$1 - b - g \neq 0$$ Also, for economic stability, usually $0 < b < 1$ and $g$ should be such that $1 - b - g > 0$ to ensure a positive multiplier and stable equilibrium. **Final answers:** - Number of endogenous variables: 2 ($Y$ and $C$). - Economic meaning of $g$: Marginal propensity of government spending with respect to income. - Equilibrium income: $$Y^* = \frac{A - bY_0 + I_0}{1 - b - g}$$ - Restriction: $$1 - b - g \neq 0$$ and preferably $$1 - b - g > 0$$ for stability.