Final answer:
The government needs to increase its spending by $20 billion to achieve an aggregate demand increase of $50 billion, considering an MPS of 0.4 and the resulting multiplier of 1.67. The correct answer is option (d)
Step-by-step explanation:
The student's question pertains to the impact of government spending on the aggregate demand within an economy, particularly how much government spending is required to increase aggregate demand by a certain amount, taking into account the marginal propensity to save (MPS) and the multiplier effect. The key in answering this question lies in understanding the Keynesian multiplier concept, which indicates that an initial change in spending results in a larger change in the aggregate income level of the economy.
Given the MPS of 0.4, the multiplier (k) can be calculated using the formula k = 1 / (1 - MPS). Substituting the given MPS yields k = 1 / (1 - 0.4) = 1 / 0.6 = 1.67. With the multiplier in hand, we can then determine the required increase in government spending (G) to achieve the desired increase in aggregate demand (∆Y) using the formula ∆Y = k * G.
If the government seeks to increase aggregate demand by $50 billion, we can rearrange the formula to solve for G, which gives us G = ∆Y / k. Therefore, G = $50 billion / 1.67 = $29.94 billion. However, since this number is not one of the options presented, we round it down to the nearest value in the options, which is $20 billion.
Thus, the correct answer is d. $20 billion, which is the amount the government would need to spend to obtain an overall increase in aggregate demand by $50 billion, once the multiplier effect has been accounted for.