# IS-LM analysis: deriving the IS curve

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IS-LM analysis: deriving the IS curve
Extension Class Presentation Ruth Tarrant

Consumption functions
Consumption (C) Income (Y) 45⁰ line Income = consumption C = a + bY a = y-intercept = autonomous consumption (i.e. the level of consumption when income is zero) b = slope of the line = marginal propensity to consume Yo At Yo, we say there is equilibrium, as consumption = income

Transferring this to Aggregate Demand
45⁰ line AD AD 1. At Yo, the goods market in the economy is in equilibrium: AD = Y 2. In equilibrium, injections = withdrawals 3. So, we can assume that Savings = Investment Yo Income

Developing the IS curve
An IS (Investments = Savings) curve shows the different combinations of income (Y) and interest rates (r) at which the goods market is in equilibrium

Aggregate Demand 45⁰ line Assume that the rate of interest in the economy is r0. At this rate of interest, aggregate demand is shown as AD1. So, when the rate of interest is r0, the goods market of the economy is in equilibrium at y0. AD1 Y0 Y0 Income Interest Rate r0 We can now plot a point on the bottom diagram, at the intersection of r0 and y0. At this point we know that the goods market in the economy is in equilibrium Income

Aggregate Demand 45⁰ line Now suppose that interest rates are lowered, to r1. Lower interest rates boost consumer spending and investment, and so AD rises. AD2 Y1 AD1 We draw a new AD curve at AD2. At this higher level of AD, the economy’s goods market equilibrium is achieved at Y1. Y0 Y0 Y1 Income Interest Rate Now we plot a point at the intersection of Y1 and r1 to indicate the point at which the goods market is in equilibrium. r0 r1 Income

If we join the dots, we create an IS curve.
Aggregate Demand 45⁰ line AD2 Y1 AD1 Y0 We can repeat this process for all interest rates, and then plot all of the relevant points on the bottom diagram. If we join the dots, we create an IS curve. Y0 Y1 Income Interest Rate IS r0 r1 Income

The slope of the IS curve
Why might the IS curve be steep? Shallow? The slope of the IS curve depends on the sensitivity of AD to interest rate changes If changes in interest rates only lead to a small change in AD, the IS curve will be steep If changes in interest rates lead to a large change in AD, the IS curve will be shallow

Shifts in the IS curve Remember, the IS curve shows the effect of interest rates in shifting AD and the resultant level of income If anything else changes, the IS curve will shift

Shifts in the IS curve What would happen to the IS curve if:
Government spending increased? Consumer confidence fell? Business optimism about future profits improved?