Solved on Jan 18, 2024

Find the equilibrium output given $Z = C + I + G$ , $C = 500 + 0.5Y$ , and $Y = Z$ with $I = 200$ and $G = 300$ .

STEP 1

Assumptions
1. The aggregate demand is defined as $Z = C + I + G$ .
2. The consumption function is given by $C = 500 + 0.5Y$ .
3. The equilibrium condition for the economy is $Y = Z$ .
4. Investment ( $I$ ) is $200$ .
5. Government spending ( $G$ ) is $300$ .

STEP 2

To find the equilibrium level of output ( $Y$ ), we need to set the production equal to the aggregate demand.
$Y = Z$

STEP 3

Substitute the expression for aggregate demand into the equilibrium condition.
$Y = C + I + G$

STEP 4

Substitute the given values for $I$ and $G$ , and the expression for $C$ into the equilibrium condition.
$Y = (500 + 0.5Y) + 200 + 300$

STEP 5

Combine like terms to simplify the equation.
$Y = 500 + 0.5Y + 200 + 300$

STEP 6

Add the constant terms on the right-hand side of the equation.
$Y = 0.5Y + 1000$

STEP 7

Subtract $0.5Y$ from both sides of the equation to solve for $Y$ .
$Y - 0.5Y = 1000$

STEP 8

Combine like terms on the left-hand side of the equation.
$0.5Y = 1000$

STEP 9

Multiply both sides of the equation by 2 to isolate $Y$ .
$Y = 1000 \times 2$

STEP 10

Calculate the value of $Y$ .
$Y = 2000$
The equilibrium level of output is $Y = 2000$ .

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Find the equilibrium output given $Z = C + I + G$ , $C = 500 + 0.5Y$ , and $Y = Z$ with $I = 200$ and $G = 300$ .

STEP 1

Assumptions
1. The aggregate demand is defined as $Z = C + I + G$ .
2. The consumption function is given by $C = 500 + 0.5Y$ .
3. The equilibrium condition for the economy is $Y = Z$ .
4. Investment ( $I$ ) is $200$ .
5. Government spending ( $G$ ) is $300$ .

STEP 2

To find the equilibrium level of output ( $Y$ ), we need to set the production equal to the aggregate demand.
$Y = Z$

STEP 3

Substitute the expression for aggregate demand into the equilibrium condition.
$Y = C + I + G$

STEP 4

Substitute the given values for $I$ and $G$ , and the expression for $C$ into the equilibrium condition.
$Y = (500 + 0.5Y) + 200 + 300$

STEP 5

Combine like terms to simplify the equation.
$Y = 500 + 0.5Y + 200 + 300$

STEP 6

Add the constant terms on the right-hand side of the equation.
$Y = 0.5Y + 1000$

STEP 7

Subtract $0.5Y$ from both sides of the equation to solve for $Y$ .
$Y - 0.5Y = 1000$

STEP 8

Combine like terms on the left-hand side of the equation.
$0.5Y = 1000$

STEP 9

Multiply both sides of the equation by 2 to isolate $Y$ .
$Y = 1000 \times 2$

STEP 10

Calculate the value of $Y$ .
$Y = 2000$
The equilibrium level of output is $Y = 2000$ .

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Find the equilibrium output given Z=C+I+GZ = C + I + GZ=C+I+G, C=500+0.5YC = 500 + 0.5YC=500+0.5Y, and Y=ZY = ZY=Z with I=200I = 200I=200 and G=300G = 300G=300.

STEP 1

STEP 2

To find the equilibrium level of output (Y Y Y), we need to set the production equal to the aggregate demand.Y=Z Y = Z Y=Z

STEP 3

Substitute the expression for aggregate demand into the equilibrium condition.Y=C+I+G Y = C + I + G Y=C+I+G

STEP 4

Substitute the given values for I I I and G G G, and the expression for C C C into the equilibrium condition.Y=(500+0.5Y)+200+300 Y = (500 + 0.5Y) + 200 + 300 Y=(500+0.5Y)+200+300

STEP 5

Combine like terms to simplify the equation.Y=500+0.5Y+200+300 Y = 500 + 0.5Y + 200 + 300 Y=500+0.5Y+200+300

STEP 6

Add the constant terms on the right-hand side of the equation.Y=0.5Y+1000 Y = 0.5Y + 1000 Y=0.5Y+1000

STEP 7

Subtract 0.5Y 0.5Y 0.5Y from both sides of the equation to solve for Y Y Y.Y−0.5Y=1000 Y - 0.5Y = 1000 Y−0.5Y=1000

STEP 8

Combine like terms on the left-hand side of the equation.0.5Y=1000 0.5Y = 1000 0.5Y=1000

STEP 9

Multiply both sides of the equation by 2 to isolate Y Y Y.Y=1000×2 Y = 1000 \times 2 Y=1000×2

STEP 10

Calculate the value of Y Y Y.Y=2000 Y = 2000 Y=2000The equilibrium level of output is Y=2000 Y = 2000 Y=2000.

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Find the equilibrium output given $Z = C + I + G$ , $C = 500 + 0.5Y$ , and $Y = Z$ with $I = 200$ and $G = 300$ .

To find the equilibrium level of output ( $Y$ ), we need to set the production equal to the aggregate demand.
$Y = Z$

Substitute the expression for aggregate demand into the equilibrium condition.
$Y = C + I + G$

Substitute the given values for $I$ and $G$ , and the expression for $C$ into the equilibrium condition.
$Y = (500 + 0.5Y) + 200 + 300$

Combine like terms to simplify the equation.
$Y = 500 + 0.5Y + 200 + 300$

Add the constant terms on the right-hand side of the equation.
$Y = 0.5Y + 1000$

Subtract $0.5Y$ from both sides of the equation to solve for $Y$ .
$Y - 0.5Y = 1000$

Combine like terms on the left-hand side of the equation.
$0.5Y = 1000$

Multiply both sides of the equation by 2 to isolate $Y$ .
$Y = 1000 \times 2$

Calculate the value of $Y$ .
$Y = 2000$
The equilibrium level of output is $Y = 2000$ .