MIU_SL - Money in the utility function Prof. Lutz Hendricks...

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Money in the utility function Prof. Lutz Hendricks August 7, 2009 L. Hendricks () Sidrauski model August 7, 2009 1 / 20
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Money in the utility function A shortcut for getting money valued in equilibrium: assume that households gain utility from holding money. "Sidrauski" model. L. Hendricks () Sidrauski model August 7, 2009 2 ± 20
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The Economic Environment Much of the model is a standard growth model. The government prints paper (costlessly). Households gain utility from holding paper. L. Hendricks () Sidrauski model August 7, 2009 3 / 20
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Household Households solve: max Z t = 0 e ρ t u ( c t , m t ) dt (1) subject to k 0 , m 0 given and p ( c + ˙ k ) + ˙ M = p ( w + rk + x ) (2) M is nominal money. m = M / p . x are lump-sum transfers (of money). L. Hendricks () Sidrauski model August 7, 2009 4 / 20
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Household Budget constraint in real terms ˙ k + ˙ M / p = w + rk + x c (3) Note that ˙ m = ˙ M / p ( M / p 2 ) ˙ p = ˙ M / p m π where π ( π = ˙ p / p ) . Therefore ˙ k + ˙ m = w + rk + x c π m (4) L. Hendricks () Sidrauski model August 7, 2009 5 / 20
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Household Budget constraint We seem to have 2 state variables ( k , m ) but only one law of motion. The reason: the correct state variable is wealth:
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MIU_SL - Money in the utility function Prof. Lutz Hendricks...

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