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Answer :
Final answer:
The equilibrium output initially is 230. When the tax rate increases, it decreases the marginal propensity to consume (MPC), leading to lower equilibrium output. However, when government spending increases to 70, it counteracts the effect of increased tax and raises equilibrium output to 270.
Explanation:
Equilibrium output in an economy is established at the point where the sum of consumption (C), investment (I), and government spending (G) is equal to the Gross Domestic Product (GDP). The consumption function, which is upward-sloping, shows the relationship between national income and consumption. The marginal propensity to consume (MPC) is the amount consumed out of an additional dollar of income, and a change in this will shift the consumption function.
In our case, the initial equilibrium output would be determined by the formula: Y = 1/(1-MPC)*(C + I + G) = 1/(1-0.5)*(50 + 15 + 50) = 230. When the tax rate increases to 0.25, the equilibrium output would still be computed with the same formula but MPC reduces because people have less disposable income due to higher taxes, that reduces consumption. Increases in government spending will shift the aggregate expenditure function up, leading to an increase in the equilibrium output. So, with increased government spending to 70, the formula becomes Y = 1/(1-MPC)*(C + I + G) = 1/(1-0.5)*(50 + 15 + 70) = 270.
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