Model Answer
0 min readIntroduction
The IS-LM model is a macroeconomic tool used to analyze the short-run equilibrium of the economy. It represents the interaction between the goods market (IS curve) and the money market (LM curve). The IS curve shows combinations of interest rates and output levels where the goods market is in equilibrium, while the LM curve represents combinations where the money market is in equilibrium. Understanding these curves and their intersection is crucial for analyzing the effects of monetary and fiscal policies. This question provides specific functions for consumption, investment, and money demand, allowing us to derive and solve for the equilibrium values of income and interest rate.
Derivation of the IS Curve
The IS curve represents equilibrium in the goods market, where aggregate demand equals aggregate supply. We can derive it using the following steps:
- Aggregate Demand (AD): AD = C + I + G
- Substitute the given functions: AD = (250 + 0.5(Y-T) - 500r) + (250 - 500r) + 200
- Simplify, given T = G = 200: AD = 250 + 0.5(Y-200) - 500r + 250 - 500r + 200
- Further simplification: AD = 250 + 0.5Y - 100 - 500r + 250 - 500r + 200
- Final AD equation: AD = 600 + 0.5Y - 1000r
- Equilibrium condition: Y = AD. Therefore, Y = 600 + 0.5Y - 1000r
- Rearrange to get the IS equation: 0.5Y = 600 - 1000r => Y = 1200 - 2000r
Thus, the IS curve equation is: Y = 1200 - 2000r
Derivation of the LM Curve
The LM curve represents equilibrium in the money market, where real money supply equals real money demand. The derivation is as follows:
- Real Money Demand (Md/P): L/P = 0.5Y – 500r
- Real Money Supply (Ms/P): Ms/P = M/P = 7650/17 = 450
- Equilibrium condition: Md/P = Ms/P. Therefore, 0.5Y – 500r = 450
- Rearrange to get the LM equation: 0.5Y = 450 + 500r => Y = 900 + 1000r
Thus, the LM curve equation is: Y = 900 + 1000r
Solving for Y and r
To find the equilibrium values of Y and r, we need to solve the IS and LM equations simultaneously:
IS: Y = 1200 - 2000r
LM: Y = 900 + 1000r
Equating the two equations:
1200 - 2000r = 900 + 1000r
300 = 3000r
r = 0.1 or 10%
Substituting r = 0.1 into either the IS or LM equation to find Y:
Y = 1200 - 2000(0.1) = 1200 - 200 = 1000
Or, Y = 900 + 1000(0.1) = 900 + 100 = 1000
Therefore, the equilibrium real income (Y) is 1000 and the equilibrium real interest rate (r) is 10%.
Conclusion
In conclusion, by deriving the IS and LM curves from the given functions and solving them simultaneously, we have determined the equilibrium real income to be 1000 and the equilibrium real interest rate to be 10%. This analysis demonstrates the power of the IS-LM model in understanding macroeconomic equilibrium and the interplay between the goods and money markets. Changes in government spending, taxes, or the money supply would shift these curves and lead to new equilibrium values, highlighting the importance of these policy tools in managing the economy.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.