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The IS/LM model combines the goods and money market equilibrium’s to form an aggregate model that describes a general equilibrium setting in the macroeconomy. This post will use a graphical approach to establish the intuition behind the building of the IS/LM framework which describes the money and goods markets. A later post will develop the IS/LM model by using matrix algebra and derivatives to analyze the interactions between the money and the goods markets in the macroeconomy.
GENERATING THE IS CURVE GRAPHICALLY
The IS curve graphically shows the relationship between the interest rate and aggregate output from the demand side of the model. The derivation of the IS curve can be taken from the dynamics of the aggregate demand function Y = C + I + G, where output (Y) is equal to consumption (C), (I) represents Income (I) and government expenditures are denoted by (G). To incorporate the interest rate into this model a slight modification will have to be made to the equation above which entails making consumption and investments a function the interest rates; Y = C(r) + I(r) + G. The graph below represents current consumption on the Y-axis and current income on the X-axis along with a graphical representation of the equation Y = C(r) + I(r) + G.
An increase in the interest rate reduces consumption as consumers put more of their disposable income into savings to take advantage of higher returns. Like consumers, businesses reduce their investment on plant and equipment with as the interest rate increases. Equilibrium in the graph above is achieved when the current income equals current consumption or Y = C(r) + I(r) + G. As the graph shows, an increase in interest rates reduces current income/output as both consumers and business reduce consumption and investment. This relationship can be visualized by plotting the real interest rate and current income, this relationship is the IS curve.
GENERATING THE LM CURVE GRAPHICALLY
The assumption is that the money supply is a fixed quantity in the short-run and is determined by the government. The demand for money is a function of prices, income/output, and the real interest rate. The money market is in equilibrium when the money supply equals money demand under the assumption of equilibrium. Using the equilibrium condition in the money market the LM curve can be derived graphically which shows the relationship between interest rates and output.
The graph above shows how an increase in income (Y) increases the demand for money. In order to restore equilibrium to the money market the interest rate increases. Similar to the IS curve, this relationship can be captured by plotting income (Y) on the X-axis and interest rate on the Y-axis This relationship derived from the money market is called the LM curve and is picture below as an increasing function of the real interest rate.
COMBINING TO GET THE IS-LM MODEL
The graph above represent the goods and money markets in the economy. The intersection of the IS and LM curves represents the macroeconomic equilibrium in the goods and money market. If either the real interest rate or output deviate from this equilibrium market forces will drive the both variables to back to their equilibrium. In a subsequent post the dynamics and interaction of the money market and the goods market will be examined through more graphical analysis. Once the intuition of the dynamics of the ISLM model has been established the topic will advance to understanding this model via matrix algebra and differential calculus.