1. Assume an economy can be modeled with these equations: |C=150+ 0.68 Ydp I=250 16=20 X=290, M=355, and T =80 What is the equilibrium Y (2 decimal
1. Assume an economy can be modeled with these equations: |C=150+ 0.68 Ydp I=250 16=20 X=290, M=355, and T =80 What is the equilibrium Y (2 decimal
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Economic Model and Equilibrium Calculation
**Objective:**
Determine the equilibrium output (\(Y\)) in a simplified economic model using the given equations.
**Given Equations:**
1. Consumption (\(C\)) is defined as:
\[
C = 150 + 0.68Y_d
\]
where \(Y_d\) is disposable income.
2. Investment (\(I\)) is given by:
\[
I = 250
\]
3. Government spending (\(G\)) is:
\[
G = 70
\]
4. Exports (\(X\)) are:
\[
X = 290
\]
5. Imports (\(M\)) amount to:
\[
M = 355
\]
6. Taxes (\(T\)) are:
\[
T = 80
\]
**Question:**
What is the equilibrium output (\(Y\)) rounded to two decimal places?
**Approach:**
To find the equilibrium output (\(Y\)), use the basic macroeconomic identity:
\[
Y = C + I + G + (X - M)
\]
Substitute \(C\) using the disposable income equation where \(Y_d = Y - T\).
- Calculate:
\[
Y_d = Y - 80
\]
\[
C = 150 + 0.68(Y - 80)
\]
\[
C = 150 + 0.68Y - 54.4
\]
\[
C = 95.6 + 0.68Y
\]
- Plug the expressions back into the equilibrium formula:
\[
Y = (95.6 + 0.68Y) + 250 + 70 + (290 - 355)
\]
\[
Y = 95.6 + 0.68Y + 250 + 70 + (-65)
\]
\[
Y = 350.6 + 0.68Y
\]
- Solving for \(Y\):
\[
Y - 0.68Y = 350.6
\]
\[
0.32Y = 350.6
\]
\[
Y =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb24b717-8ee5-4ca9-8061-74ddb7e91c1a%2F904c7029-1e01-4239-be54-d329482b0c79%2F5td9u7c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Economic Model and Equilibrium Calculation
**Objective:**
Determine the equilibrium output (\(Y\)) in a simplified economic model using the given equations.
**Given Equations:**
1. Consumption (\(C\)) is defined as:
\[
C = 150 + 0.68Y_d
\]
where \(Y_d\) is disposable income.
2. Investment (\(I\)) is given by:
\[
I = 250
\]
3. Government spending (\(G\)) is:
\[
G = 70
\]
4. Exports (\(X\)) are:
\[
X = 290
\]
5. Imports (\(M\)) amount to:
\[
M = 355
\]
6. Taxes (\(T\)) are:
\[
T = 80
\]
**Question:**
What is the equilibrium output (\(Y\)) rounded to two decimal places?
**Approach:**
To find the equilibrium output (\(Y\)), use the basic macroeconomic identity:
\[
Y = C + I + G + (X - M)
\]
Substitute \(C\) using the disposable income equation where \(Y_d = Y - T\).
- Calculate:
\[
Y_d = Y - 80
\]
\[
C = 150 + 0.68(Y - 80)
\]
\[
C = 150 + 0.68Y - 54.4
\]
\[
C = 95.6 + 0.68Y
\]
- Plug the expressions back into the equilibrium formula:
\[
Y = (95.6 + 0.68Y) + 250 + 70 + (290 - 355)
\]
\[
Y = 95.6 + 0.68Y + 250 + 70 + (-65)
\]
\[
Y = 350.6 + 0.68Y
\]
- Solving for \(Y\):
\[
Y - 0.68Y = 350.6
\]
\[
0.32Y = 350.6
\]
\[
Y =
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