and the LM equations. Calculate the equilibrium interest ra taxes are cut by 20% and the money supply is held constant interest rate and level of income? that the Federal Reserve changes the money supply to hold t. What is the new level of income? What must the new mo

ENGR.ECONOMIC ANALYSIS
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### Understanding Economic Equilibrium: A Case Study

In this case study, we examine the economic equilibrium using a hypothetical economy described by the following equations:

**Consumption Function:**
\[ C = 500 + 0.75 (Y - T) \]
Where:
- \( C \) is consumption
- \( Y \) is income
- \( T \) is taxes

**Investment Function:**
\[ I = 1000 - 50r \]
Where:
- \( I \) is investment
- \( r \) is the interest rate

**Money Market Equilibrium Condition:**
\[ \frac{M}{P} = Y - 200r \]
Where:
- \( M \) is the money supply
- \( P \) is the price level

**Government Expenditure:**
\[ G = 1000 \]

**Taxes:**
\[ T = 1000 \]

**Money Supply:**
\[ M = 6000 \]

**Price Level:**
\[ P = 2 \]

### Questions:

**a. Derive the IS and LM equations. Calculate the equilibrium interest rate and level of income.**

**b. Suppose that taxes are cut by 20% and the money supply is held constant. What are the new equilibrium interest rate and level of income?**

**c. Suppose that the Federal Reserve changes the money supply to hold the interest rate constant. What is the new level of income? What must the new money supply be?**

**d. Suppose the Federal Reserve changes the money supply to hold the level of income constant. What is the new equilibrium interest rate? What must the money supply be?**

By exploring these questions, students can gain a deeper understanding of how fiscal and monetary policies impact the equilibrium in an economy, and how different variables interact within the IS-LM framework.
Transcribed Image Text:### Understanding Economic Equilibrium: A Case Study In this case study, we examine the economic equilibrium using a hypothetical economy described by the following equations: **Consumption Function:** \[ C = 500 + 0.75 (Y - T) \] Where: - \( C \) is consumption - \( Y \) is income - \( T \) is taxes **Investment Function:** \[ I = 1000 - 50r \] Where: - \( I \) is investment - \( r \) is the interest rate **Money Market Equilibrium Condition:** \[ \frac{M}{P} = Y - 200r \] Where: - \( M \) is the money supply - \( P \) is the price level **Government Expenditure:** \[ G = 1000 \] **Taxes:** \[ T = 1000 \] **Money Supply:** \[ M = 6000 \] **Price Level:** \[ P = 2 \] ### Questions: **a. Derive the IS and LM equations. Calculate the equilibrium interest rate and level of income.** **b. Suppose that taxes are cut by 20% and the money supply is held constant. What are the new equilibrium interest rate and level of income?** **c. Suppose that the Federal Reserve changes the money supply to hold the interest rate constant. What is the new level of income? What must the new money supply be?** **d. Suppose the Federal Reserve changes the money supply to hold the level of income constant. What is the new equilibrium interest rate? What must the money supply be?** By exploring these questions, students can gain a deeper understanding of how fiscal and monetary policies impact the equilibrium in an economy, and how different variables interact within the IS-LM framework.
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