Derive IS and LM curves. How does an economy achieve equilibrium in both real sector and monetary sector?
In introductory macroeconomics, the IS-LM model is a critical tool used to understand the interaction between the real and monetary sectors of the economy. The model helps to determine the equilibrium levels of output and interest rates by combining two distinct relationships: the IS curve, which represents equilibrium in the goods market, and the LM curve, which represents equilibrium in the money market. The IS-LM model is based on Keynesian principles, where the economy is analyzed in the short run, assuming that prices are fixed and output is determined by aggregate demand.
### Derivation of the IS Curve
The IS curve represents the combinations of interest rates and levels of output where the goods market is in equilibrium. The goods market is in equilibrium when aggregate demand equals output (or income), meaning there is no unplanned inventory accumulation.
Aggregate Demand is composed of the following components:
1. Consumption (C): A function of disposable income, typically represented as \( C = C(Y - T) \), where \( Y \) is national income and \( T \) is taxes. The consumption function reflects the relationship between national income and consumption expenditure.
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