Model Answer
0 min readIntroduction
The IS-LM model, developed by John Hicks and Alvin Hansen, is a foundational macroeconomic tool used to analyze the relationship between interest rates, output, and the money market. It provides a framework for understanding how monetary and fiscal policies affect the economy. Determining the equilibrium national income and interest rate is crucial for policymakers aiming to stabilize the economy and achieve full employment. This question tests the candidate’s ability to apply this model to a given set of economic conditions and assess the impact of monetary policy changes.
Deriving the IS Equation
The IS curve represents the equilibrium in the goods market. We start with the equilibrium condition where Aggregate Saving (S) equals Investment (I): S = I.
Substituting the given functions:
-40 + 0.5(Y - T) + 0.25r = 20 - 0.25r
Substituting the tax function T = 20 + 0.2Y:
-40 + 0.5(Y - (20 + 0.2Y)) + 0.25r = 20 - 0.25r
-40 + 0.5(0.8Y - 20) + 0.25r = 20 - 0.25r
-40 + 0.4Y - 10 + 0.25r = 20 - 0.25r
0.4Y + 0.5r = 70
Therefore, the IS equation is: Y = 175 - 1.25r
Deriving the LM Equation
The LM curve represents the equilibrium in the money market. The equilibrium condition is where Money Demand (L) equals Money Supply (M): L = M.
Substituting the given functions:
0.4Y - 0.5r = 40
Therefore, the LM equation is: Y = 100 + 1.25r
Calculating Equilibrium National Income (Y) and Interest Rate (r)
To find the equilibrium, we solve the IS and LM equations simultaneously:
175 - 1.25r = 100 + 1.25r
75 = 2.5r
r = 30
Substituting r = 30 into either the IS or LM equation to find Y:
Y = 100 + 1.25(30) = 100 + 37.5 = 137.5
Therefore, the equilibrium national income (Y) is 137.5 crore rupees and the equilibrium interest rate (r) is 30%.
Impact of Increased Money Supply
When the money supply increases by ₹20 crore, the new money supply (M’) becomes 60 crore rupees. The LM equation shifts to the right:
0.4Y - 0.5r = 60
Therefore, the new LM equation is: Y = 150 + 1.25r
Solving the IS and new LM equations simultaneously:
175 - 1.25r = 150 + 1.25r
25 = 2.5r
r = 10
Substituting r = 10 into the IS equation:
Y = 175 - 1.25(10) = 175 - 12.5 = 162.5
Therefore, with the increased money supply, the new equilibrium national income (Y) is 162.5 crore rupees and the new equilibrium interest rate (r) is 10%.
The increase in money supply has led to a decrease in the interest rate and an increase in the national income, demonstrating the expansionary effect of monetary policy.
Conclusion
In conclusion, using the IS-LM model, we determined the initial equilibrium national income to be ₹137.5 crore and the interest rate to be 30%. An increase in the money supply by ₹20 crore resulted in a new equilibrium with a national income of ₹162.5 crore and an interest rate of 10%. This illustrates the inverse relationship between money supply and interest rates, and the positive relationship between interest rates and national income, as predicted by the model. The effectiveness of this monetary policy depends on the slope of the IS and LM curves, and other factors not considered in this simplified model.
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.