Final answer:
In a closed economy, the equilibrium income level is $825 billion. If government purchases are reduced by $100 billion, the new equilibrium income level will be $775 billion. The multiplier for this economy is 4.
Step-by-step explanation:
In a closed economy with no trade, net exports are equal to zero. The consumption function is given by C = $25 billion + 0.75(Y - T), where Y is income, Iₚ is planned investment, G is government purchases, and T is taxes. Given that G = $130 billion, Iₚ = $60 billion, and T = $20 billion, we can calculate the equilibrium income level by setting planned expenditure (Y = C + Iₚ + G) equal to income. By substituting the given values and solving the equation, the equilibrium income level is $825 billion.
If government purchases are reduced by $100 billion, we can calculate the new equilibrium level of income by substituting the new value of G into the equation Y = C + Iₚ + G. The new equilibrium income level will be $775 billion.
The multiplier for this economy can be calculated by using the formula for the spending multiplier: 1 / (1 - MPC), where MPC is the marginal propensity to consume. In this case, MPC is 0.75, so the multiplier is equal to 4. This means that a $1 decrease in government purchases will decrease the equilibrium income level by $4.