ec3332-SemI2011-2012Lec3

ec3332-SemI2011-2012Lec3 - Money and Banking I EC3332 Sem...

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Money and Banking I EC3332 Sem I, 2011-12 Lec 3: Money and Capital
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Objective In the OLG model with fiat money: savings can be held only in fiat money. In reality, there are several assets that can be used to store value – e.g. land, capital, etc. In this chapter: capital as one particular alternative.
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The model
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Capital Production technology: k t x k t Time: t t + 1 where x>0. Capital goods produce only once before disintegrating: “One horse shay” Depreciation rate = 100% Transformation
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Assumptions Endowments: y units of consumption good when young. Population grows at the gross rate n. Each member of the initial old begins with a stock of capital that produces xk 0 goods in the first period
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Non-monetary equilibrium
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Equilibrium without Fiat Money Budget constraint when young: (6.1) Let x be gross interest rate (1+net interest rate) Budget constraint when old: (6.2)
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Lifetime Budget Constraint Lifetime budget constraint: (6.3)
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Choice of Capital
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Diminishing Marginal Product Alternative assumption: diminishing marginal product of capital. As capital increases, the added output from an extra unit of capital gets smaller. Total output still rises as long as the marginal product of capital is positive.
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Marginal Product of Capital Output as a function f ( k ) of capital. Marginal product of capital: f’ ( k )
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Budget constraints Budget constraint when young: Budget constraint when old: Combine these two inequalities:
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The slope of the “budget line” The slope is negative: It is decreasing, i.e. it becomes steeper.
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Golden rule allocations
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What would be the allocation chosen by a benevolent planner? Goods available for use in period t : Output from capital Endowments of the young Total use of the consumption goods: Consumption by the young. Consumption by the old.
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Feasible set Divide by N t and focus on stationary allocations: Or, equivalently,
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Net domestic product Output net of the costs of investment: The planner will choose k in order to maximize net domestic product: This is the golden-rule capital stock.
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Golden rule for capital accumulation Marginal product of capital = Rate of growth of population.
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This note was uploaded on 01/30/2012 for the course ECON 121 taught by Professor Abi during the Spring '11 term at Abu Dhabi University.

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ec3332-SemI2011-2012Lec3 - Money and Banking I EC3332 Sem...

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