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Unformatted text preview: Cash in Advance Models Prof. Lutz Hendricks August 6, 2009 L. Hendricks () Cash in Advance Models August 6, 2009 1 / 35 Cashinadvance Models We study a second model of money. OLG models have 2 shortcomings: 1 They fail to explain rate of return dominance. 2 Money has no transaction value. CIA models focus on transactions demand for money. L. Hendricks () Cash in Advance Models August 6, 2009 2 / 35 The CIA Model L. Hendricks () Cash in Advance Models August 6, 2009 3 / 35 Model Outline The overall model structure is that of the standard growth model. The &rm hires K and L from the household. A single representative household: works for the &rm saves in the form of money and capital The transaction technology requires that some goods are purchased with money . L. Hendricks () Cash in Advance Models August 6, 2009 4 / 35 Timing within periods 1 The household enters the period with capital k t and a stock of money m d t & 1 . 2 He then receives a transfer of money τ t from the government. His period t money holdings are m t = m d t & 1 + τ t 3 The household produces and sells his output for money to be received at the &end of the period.¡ 4 He uses m t to buy goods from other households ( c t and k t + 1 ). 5 The household is paid for the goods he sold in step 3 so that his end of period money stock is m d t . Note that money earned in period t cannot be used until t + 1 . L. Hendricks () Cash in Advance Models August 6, 2009 5 / 35 Household problem We simply add one constraint to the household problem: the CIA constraint. The household solves max ∑ ∞ t = 1 β t u ( c t ) subject to the budget constraint k t + 1 + c t + m d t / p t = f ( k t ) + ( 1 & δ ) k t + m t / p t and the CIA constraint m t / p t ¡ c t + k t + 1 & ( 1 & δ ) k t and the law of motion m t + 1 = m d t + τ t + 1 L. Hendricks () Cash in Advance Models August 6, 2009 6 / 35 Household problem Remarks Exactly what kinds of goods have to be bought with cash is arbitrary. The CIA constraint holds with equality if the rate of return on money is less than that on capital (the nominal interest rate is positive). L. Hendricks () Cash in Advance Models August 6, 2009 7 / 35 Houshold: Dynamic Program Individual state variables: m , k . Bellman equation: V ( m , k ) = max u ( c ) + β V ( m , k ) + λ ( BC ) + γ ( CIA ) We need to impose m t = m d t & 1 + τ t Then we can use m t + 1 as a control (this would not work under uncertainty)....
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