Consider the following economyC=1000+0.4(Y-T)I=500T=400G=300The current administration wants to expand the economy through fiscal policy. It chooses to change government spending (not touching taxes at all). The target income of equilibrium is 3,000. By how much should the government change spending to achieve that goal? Assume that the other components of autonomous spending remain the same.  (Note that I asked change in government spending, not level. If the change is negative, you should precede your answer by a minus sign. You should figure out the new level of autonomous spending that would achieve that goal and subtract the old level of autonomous spending.)

To achieve the target income of equilibrium of 3,000, we need to determine the change in government spending.

First, let's calculate the current level of autonomous spending. Autonomous spending is the sum of consumption (C) and investment (I) when income (Y) is zero.

Given: C = 1000 + 0.4(Y - T) I = 500 T = 400 G = 300

When Y is zero, we can substitute it into the consumption function: C = 1000 + 0.4(0 - 400) C = 1000 + 0.4(-400) C = 1000 - 160 C = 840

The current level of autonomous spending is 840 + 500 = 1340.

Next, we need to find the change in government spending required to reach the target income of 3,000. Let's denote the change in government spending as ΔG.

The target income of equilibrium is given as 3,000, so we can set up the equation: Y = C + I + G

Substituting the values: 3,000 = (1000 + 0.4(Y - T)) + 500 + G

Simplifying the equation: 3,000 = 1000 + 0.4Y - 0.4T + 500 + G

Rearranging the terms: 0.4Y - 0.4T + G = 3,000 - 1000 - 500

0.4Y - 0.4T + G = 1,500

Since we want to achieve the target income of 3,000, we can substitute Y = 3,000 into the equation: 0.4(3,000) - 0.4T + G = 1,500

1,200 - 0.4T + G = 1,500

Rearranging the terms: -0.4T + G = 1,500 - 1,200

-0.4T + G = 300

Now, we can substitute the current level of autonomous spending (1340) into the equation: -0.4T + G = 300

-0.4T + G = 300 - 1340

-0.4T + G = -1,040

To achieve the target income of 3,000, the government should decrease spending by 1,040 units.

To achieve the target income of equilibrium of 3,000, we need to determine the change in government spending.

Given the equation for consumption (C) as C = 1000 + 0.4(Y - T), investment (I) as I = 500, taxes (T) as 400, and government spending (G) as 300, we can calculate the current level of autonomous spending.

Autonomous spending is the sum of consumption and investment when income (Y) is zero. Therefore, we can substitute Y = 0 into the consumption equation to find the autonomous consumption (C0):

C0 = 1000 + 0.4(0 - 400) C0 = 1000 + 0.4(-400) C0 = 1000 - 160 C0 = 840

The current level of autonomous spending is 840.

To achieve the target income of 3,000, we need to find the change in government spending (ΔG). We can rearrange the equation for income (Y) as follows:

Y = C + I + G 3,000 = (1000 + 0.4(Y - T)) + 500 + G

Substituting the given values for T and G:

3,000 = (1000 + 0.4(Y - 400)) + 500 + 300

Simplifying the equation:

3,000 = 1000 + 0.4Y - 160 + 500 + 300 3,000 = 1,840 + 0.4Y

Rearranging the equation to solve for Y:

0.4Y = 3,000 - 1,840 0.4Y = 1,160 Y = 1,160 / 0.4 Y = 2,900

The new level of income (Y) required to achieve the target is 2,900.

To find the change in government spending (ΔG), we subtract the old level of autonomous spending (840) from the new level of autonomous spending (2,900):

ΔG = 2,900 - 840 ΔG = 2,060

Therefore, the government should increase spending by 2,060 to achieve the target income of equilibrium.