The graph above shows the AD, LRAS, and SRAS functions for a country. The Fed is following an inflation targeting policy. Its target inflation rate is Π* = 5.00 percent and the potential GDP equals YP = 100,000. The Fed is quite successful in achieving its inflation target in the long run. Okun's alpha equals 2. Currently the economy is in the state of long-run equilibrium. Marginal propensity to consume is MPC = 0.80. The government increases transfer payments (TR) by 4,000 units and finances it through an equal increase in taxes (TX).

If the Fed does not follow the inflation targeting policy, and if the increases in TR and TX turn out to be permanent, private spending will be crowded out by X units. What is the value of X?

Question

The graph above shows the AD, LRAS, and SRAS functions for a country. The Fed is following an inflation targeting policy. Its target inflation rate is Π* = 5.00 percent and the potential GDP equals YP = 100,000. The Fed is quite successful in achieving its inflation target in the long run.  Okun's alpha equals 2. Currently the economy is in the state of long-run equilibrium. Marginal propensity to consume is MPC = 0.80. The government increases transfer payments (TR) by 4,000 units and finances it through an equal increase in taxes (TX).

If the Fed does not follow the inflation targeting policy, and if the increases in TR and TX turn out to be permanent, private spending will be crowded out by X units.  What is the value of X?

BlackTom AI · Accepted Answer

We begin by restating the given information and the question context to frame the analysis. The problem provides that the Fed targets a long-run inflation rate of Π* = 5.00%, potential GDP YP = 100,000, Okun's alpha = 2, MPC = 0.80, and that the government increases transfer payments (TR) by 4,000 financed by an equal tax increase (TX). If the Fed does not follow the inflation targeting policy and if the TR and TX increases are permanent, private spending will be crowded out by X units. We are asked for the value of X.

Option 1: 1,000. The crowding out value depends on the fiscal multiplier and the marginal propensity to consume, along with any Ricardian or balanced-budget effects. With MPC = 0.80, the simple fiscal spending multiplier for an equal increase in TR financed by TX under a balanced budget is roughly 1/(1 − MPC) minus some consideration of tax offsets. If TR increases by 4,000 and TX increases by the same amount, the net effect on disposable income is the change in TR minus the tax offset times the MPC, which yields a relatively modest crowding out, but 1,000 is quite small given a 4,000 stimulus and a high MPC. This option seems too small unless there are stabilizing automatic mechanisms or other offsets, which aren’t specified here. Therefore, 1,000 under the stated assumptions is unlikely.

Option 2: 2,000. This value is larger than 1,000 but still relatively small given the 4,000 stimulus in a closed economy with MPC = 0.80. To produce a crowding-out of 2,000, the net impact on private spending would have to be dampened by tax effects and the crowding-out mechanism. However, with a balanced increase in TR and TX, a significant portion of the stimulus is saved or offset through tax-induced changes in consumption, yet the proportionality to 4,000 would typically lead to a larger crowding-out effect than 2,000 unless there are countervailing monetary actions or velocity changes. Without additional details supporting a 2,000 outcome, this option is questionable.

Option 3: 3,000. A crowding-out amount of 3,000 is more consistent with a substantial but not full offset of the 4,000 increase in government spending via the tax-financed transfer. Given MPC = 0.80, a sizable portion of the TR increase would be spent, but the equal tax increase would dampen disposable income by about 0.8 per dollar, reducing consumption by about 0.8 × 4,000 = 3,200 in the simplest interpretation. Since 3,200 is larger than 3,000, this could be plausible if some of the induced consumption is offset by other channels or if the multiplier effects are limited. However, the exact crowding-out figure would depend on the interaction with monetary policy and the fixed price level assumptions, making 3,000 less certain but still plausible depending on the model specifics.

Option 4: 4,000. With a balanced-budget fiscal expansion (TR up by 4,000 and TX up by 4,000), the net increase in after-tax income depends on how much of TR translates into additional consumption versus savings, given MPC = 0.80. A common first-step approach shows that the direct effect on private spending is MPC × (change in disposable income) = 0.80 × (TR − TX) = 0.80 × 0 = 0 if TR and TX rise by the same amount exactly. However, the problem states that private spending will be crowded out by X units if the Fed does not follow the inflation-targeting policy and if TR and TX increases are permanent. In many standard macro models with a balanced-budget multiplier under a fixed price level and no additional monetary offset, the balanced-budget multiplier is 1: private spending increases by the full amount of the government spending increase when financed by an equal tax increase, but the presence of MPC and the crowding-out effect due to higher interest rates or crowding out of private investment can lead to a partial offset. In typical simple models, the crowding-out effect equals the size of the government spending increase, especially when the tax increase fully offsets the revenue, leading to a complete offset of the private spending effect at the multiplier level. Given the problem’s explicit assertion that private spending will be crowded out by X units when TR and TX rise permanently, and given the numeric setup with TR = TX = 4,000, the most direct interpretation in many introductory macro problem settings is that the crowding-out amount X equals the increase in transfer payments, i.e., 4,000. This aligns with the option that directly matches the problem’s stated numeric pairing and the typical balanced-budget crowding-out intuition under permanent changes with high MPC. Therefore, X = 4,000 is consistent with the problem’s framing under the stated permanent increases and crowding-out mechanism.

Option 5: None of the above. This would be the choice if all the prior options failed to capture the correct crowding-out amount under the given assumptions. However, given the problem’s explicit numbers and typical balanced-budget crowding-out intuition, one of the options (namely 4,000) aligns with the expected result. Hence, selecting None of the above would not be appropriate.

Summary of the per-option reasoning shows that Option 4, 4,000, best matches the standard interpretation of crowding-out in a balanced-budget scenario with permanent TR and TX increases and a high MPC, given the problem’s description. However, the essential takeaway is to trace the mechanism: a permanent equal increase in TR and TX reduces the net disposable income impact through taxes, dampens private consumption via MPC, and leads to a crowding-out amount that, in this setup, is typically equal to the policy-induced net effect, which the problem states as X.

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