Could you please help me with these couple of problems?
Assume that C=a+(.75)(YD), where YD= Y-T
1. If the autonomous tax increases by 1000, the leakage schedule will shift up by how much?
2. A full employment income, planned aggregate expenditure exceeds income by 1000, what is the change required in G necessary to have equilibrium occur at full employment income?
3. A full employment income, planned aggregate expenditure exceeds income by 1000, what is the change required in T necessary to have equilibrium occur at full employment income?
4. At full employment income, planned aggregate expenditure exceeds income by 1000. The difference between the current equilibrium income and full employment income equals?
I'm not sure what you mean by "leakage schedule" That said, your marginal propensity to consume is .75, meaning your government spending multiplier is 1/(1-.mpc) = 1/.25 = 4. The taxation multiplier is one less than the government spending multiplier = 3.
So, if taxes go up by $1000, income drops by 3*1000 = 3000.
2) use the government multiplier
3) Use the taxation multiplier.
4) ?? Is the question: "if the A is 1000 more than B, what is the difference between A and B"?
Sure, I can help you with these problems. Let's break them down one by one:
1. To determine how the leakage schedule will shift when the autonomous tax increases by 1000, we need to understand the relationship between the autonomous tax and the leakage schedule. In this case, the leakage schedule is represented by C, which is equal to a + (0.75)(YD).
Since YD = Y - T, an increase in autonomous tax (TA) by 1000 would result in a decrease in disposable income (YD) by 1000. Therefore, we can substitute YD with (Y - T) - 1000 in the leakage schedule equation.
The new leakage schedule (C') can be represented as follows:
C' = a + (0.75)(YD - 1000)
= a + (0.75)((Y - T) - 1000)
Therefore, the leakage schedule will shift up by 1000, resulting in a decrease in consumption (C) by 0.75 times the decrease in disposable income (1000).
2. To determine the change required in government spending (G) necessary to achieve equilibrium at full employment income, we need to understand the relationship between planned aggregate expenditure (PAE) and income (Y).
Equilibrium occurs when PAE equals income (Y). In this case, PAE exceeds income by 1000. Therefore, to achieve equilibrium at full employment income, we need to decrease PAE by 1000.
Since planned aggregate expenditure (PAE) is composed of consumption (C), investment (I), government spending (G), and net exports (NX), we can adjust the equation to find the change required in G:
PAE = C + I + G + NX
Y = PAE
To achieve equilibrium at full employment income, we modify the equation as follows:
Y = C + I + G + NX
Y = C - 1000 + I + G + NX
Therefore, the change required in government spending (G) necessary to achieve equilibrium at full employment income is an increase of 1000.
3. To determine the change required in taxes (T) necessary to achieve equilibrium at full employment income, we can follow a similar approach to the previous question.
Since planned aggregate expenditure (PAE) is composed of consumption (C), investment (I), government spending (G), and net exports (NX), we can adjust the equation to find the change required in T:
PAE = C + I + G + NX
Y = PAE
To achieve equilibrium at full employment income, we modify the equation as follows:
Y = C + I + G + NX
Y = C + I + G - 1000 + NX
Therefore, the change required in taxes (T) necessary to achieve equilibrium at full employment income is a decrease of 1000.
4. To determine the difference between the current equilibrium income and full employment income when PAE exceeds income by 1000, we need to compare the two income levels.
At full employment income, PAE and income are equal, meaning there is no difference:
Y = PAE
However, in the current situation where PAE exceeds income by 1000, we modify the equation as follows:
Y = PAE - 1000
Therefore, the difference between the current equilibrium income and full employment income is 1000.