Question

Suppose when Y increases from 500 to 1000, consumption increases from 450 to 850, and taxes increase from 20 to 70. Then private saving increases from 30 to 80 and the marginal tax rate is 1/10.

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Answer 1

To find the equilibrium for this economy, we set total spending equal to the potential GDP. The equilibrium national income is approximately $3916.67. To achieve the potential GDP level of 3500, a decrease in government spending of approximately $62.50 is needed.

Step-by-step explanation:

To find the equilibrium for this economy, we need to set the total spending (aggregate demand) equal to the potential GDP. Aggregate demand is given by the equation C + I + G + X - M, where C is consumption, I is investment, G is government spending, X is exports, and M is imports. Plugging in the given values, we have:

C + 300 + 200 + 500 - 0.1(Y - T) = 3500

Now, we substitute the equations for consumption and taxes:

450 + 0.85(Y - 0.25Y) + 300 + 200 + 500 - 0.1(Y - 0.25Y) = 3500

Simplifying, we get:

1150 + 0.6Y = 3500

0.6Y = 2350

Y = 3916.67

So the equilibrium national income is approximately $3916.67.

To find the change in government spending needed to achieve the potential GDP level of 3500, we can use the multiplier approach. The multiplier is given by 1/(1 - MPC), where MPC is the marginal propensity to consume (the fraction of additional income that is spent). In this case, the MPC is 0.85. Plugging in the values, we have:

Multiplier = 1/(1 - 0.85) = 1/(0.15) = 6.67

Since we want the increase in government spending to result in an increase in national income of 3500 - 3916.67 = -416.67 (negative because we're moving towards the equilibrium), we divide this change by the multiplier:

Change in Govt Spending = -416.67 / 6.67 = -62.50

So a decrease in government spending of approximately $62.50 is needed to achieve the potential GDP level.