Lecture 2 - Capital Markets and Time

Lecture 2 - Capital Markets and Time - Econ 104B Capital...

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Econ 104B Capital Markets and Time
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Capital The capital stock of an economy is the sum total of machines, buildings, and other reproducible resources in existence at a point in time represent some part of the economy’s past output that was set aside for future production
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Rate of Return Time Consumption t 1 t 2 t 3 c 0 s x its long-run level ( c ) in
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Rate of Return The single period rate of return ( r 1 ) on an investment is the extra consumption provided in period 2 as a fraction of the consumption forgone in period 1 1 1 - = - = s x s s x r
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Rate of Return Time Consumption t 1 t 2 t 3 c 0 s s is used to produce additional output in all future periods y
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Rate of Return The perpetual rate of return ( r ) is the permanent increment to future consumption expressed as a fraction of the initial consumption foregone s y r =
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Rate of Return When economists speak of the rate of return to capital accumulation, they have in mind something between these two extremes a measure of the terms at which consumption today may be turned into consumption tomorrow
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Rate of Return and Price of Future Goods Assume that there are only two periods The rate of return between these two periods ( r ) is defined to be 1 0 1 - = c c r Rewriting, we get r c c + = 1 1 1 0
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Rate of Return and Price of Future Goods The relative price of future goods ( p 1 ) is the quantity of present goods that must be foregone to increase future consumption by one unit r c c p + = = 1 1 1 0 1
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Demand for Future Goods An individual’s utility depends on present and future consumption
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Utility Maximization Current consumption Future Consumption w w / p 1 0 1 choosing to consume c * currently and c 0 * c 1 *
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Utility Maximization • The individual consumes c 0 * in the present period and chooses to save w - c 0 * to consume next period This future consumption can be found from the budget constraint p c * = W - c *
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Intertemporal Impatience Individuals’ utility-maximizing choices over time will depend on how they feel about waiting for future consumption
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Intertemporal Impatience Assume that an individual’s utility function for consumption [ U ( c )] is the same for both periods but period 1’s utility is discounted by a “rate of time preference” of 1/(1+ δ ) (where δ >0)
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Lecture 2 - Capital Markets and Time - Econ 104B Capital...

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