巴罗宏观经济学：现代观点第7章共44页

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Consumption and Saving
Household chooses the time path of consumption—in this case, C1 and C2— to maximize utility, subject to the budget constraint.
p.v. of consumption = value of initial assets + p.v. of wage incomes − p.v. of assets end year 2
V = (1 + i0)·(B0/P+K0) + (w/P)1·L + (w/P)2·L/(1+i1)
p.v. of sources of funds = value of initial assets + p.v. of wage incomes
B2/P + K2 = (1+ i1) ·(B1/P + K1) + (w/P)2 ·L − C2
B2/P + K2 = (1+i1) ·[(1+i0)·( B0/P + K0) + (w/P)1·L − C1] + (w/P)2 ·L − C2
Macroeconomics Chapter 7
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Year2 C2 + ( B2/ P + K2) − ( B1/ P + K1) = ( w/ P) 2 ·L + i1 ·( B1/ P + K1) consumption in year 2 + real saving in year 2 = real income in year 2
Macroeconomics Chapter 7
Dollars received or spent in year 2 must be discounted to make them comparable to dollars in year 1.
The term 1+i1 is called a discount factor.
Macroeconomics Chapter 7
Consumption and Saving
Household budget constraint
C + (1/P) ·∆B+ ∆K = π/P + ( w/P )·L + i·( B/P + K)
π /P = 0 C+(1/P)·∆B+∆K=(w/P)·L+i·(B/P+K) consumption+ real saving = real income
B1/P + K1 = B0/P + K0 + i0·(B0/P + K0) + ( w/P)1·L− C1
Real assets end year1 = real assets end year0 + real income year1 − consumption year1
Macroeconomics Chapter 7
Macroeconomics Chapter 7
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Consumption and Saving
Macroeconomics Chapter 7
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Consumption and Saving
Consumption Over Two Years
Year1 C1 + ( B1/ P + K1) − ( B0/ P + K0) = ( w/P)1 ·L + i0 ·( B0/ P + K0) consumption in year1 + real saving in year1 = real income in year1
Consumption and Saving
Consumption wenku.baidu.comver Two Years
C2+(1+i1)·C1 = (1+i1)·(1+i0)·(B0/P+K0) +(1+i1)·(w/P)1·L+(w/P)2·L - (B2/P + K2)
Two-year household budget constraint:
C1 + C2/(1+i1) = (1+ i0)·(B0/P+K0) + (w/P)1·L+(w/P)2·L/(1+i1)−(B2/P+K2)/(1+i1)
Macroeconomics Chapter 7
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Consumption and Saving
Present value
If the interest rate, i1, is greater than zero, $1 received or spent in year 1 is equivalent to more than $1 in year 2.
Macroeconomics Chapter 7
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Consumption and Saving
Choosing consumption: income effects
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Consumption and Saving
Macroeconomics Chapter 7
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Consumption and Saving
Macroeconomics Chapter 7
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Consumption and Saving
Consumption Over Two Years
B1/P + K1 = (1+i0) ·(B0/P + K0) + (w/P)1 ·L − C1
Macroeconomics Chapter 7
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Consumption and Saving
Choosing consumption: income effects
C1 + C2/(1+i1) = (1+ i0)·(B0/P+K0) + (w/P)1·L+(w/P)2·L/(1+i1)−(B2/P+K2)/(1+i1)
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Consumption and Saving
Consumption Over Two Years
Combine the budget constraints to describe a household’s choice between consuming this year, C1, and next year, C2.