ch10notes - The IS Curve Major building block of the...

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The IS Curve Major building block of the short-run model Short-run: Interest rate is set by the Fed High interest rates decrease investment spending. Less investment spending causes a decrease in real GDP. National Income Identity t t t t t t IM EX G I C Y - + + + = Consumption t c t Y a C = Consumption is a fixed fraction of potential output. Consumption is not related to short-run output. Roughly 2/3 of spending on GDP is from consumption.
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Government Spending t g t Y a G = Exports t ex t Y a EX = Imports t im t Y a IM = These spending items are related to long-run, or potential GDP. They are independent of t Y ~ , holding t Y fixed.
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Investment Spending Firms borrow to finance purchases of additional capital. Firms borrow at the real interest rate, R t . The marginal product of capital is r . The value of r is determined by the long-run model. In balanced growth, investment is a fixed fraction of GDP. When will there be an unusually large amount of investment? Suppose that % 10 and % 5 = = r R t . Consider buying 100 units of new capital. Produces output of 10 units per year. Pay 5 units of output in interest on borrowing → more profits.
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Formalize as: ) ( r R b a Y I t i t t - - = When , r R t = then t i t Y a I = . When t i t t Y a I r R < then , . When t i t t Y a I r R < then , . However, costs of quickly installing K allows for finite b . Now divide the national income identity by t Y t t t t t t t t t t t t Y IM Y EX Y G Y I Y C Y Y - + + + = , or: im ex g t i c t t a a a r R b a a Y Y - + + - - + = ) (
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Next, subtract t t Y Y / 1 = from both sides.
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