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[size=11.000000pt]Suppose [size=11.000000pt]n [size=11.000000pt]= 1. Suppose the endowment grows, i.e. [size=11.000000pt]ω[size=8.000000pt]t [size=11.000000pt]= ([size=11.000000pt]y[size=8.000000pt]t[size=11.000000pt], [size=11.000000pt]0) where [size=11.000000pt]y[size=8.000000pt]t [size=11.000000pt]= [size=11.000000pt]Ay[size=8.000000pt]t[size=8.000000pt]−[size=8.000000pt]1[size=11.000000pt], and [size=11.000000pt]A > [size=11.000000pt]1 is aconstant. Also, [size=11.000000pt]ω[size=8.000000pt]1 [size=11.000000pt]= ([size=11.000000pt]y,[size=11.000000pt]0). There is a constant amount of fiat money [size=11.000000pt]M[size=11.000000pt]. Suppose the preferences of generations 1, 2, ..., are
u(c1, c2) = √c1 + √c2,  and those of the IO are uIO(c2) = c2.



                                                                                                               

                                               
•                                                         Write down equations that represent the budget constraints in the first and second periodof a typical individual from generation [size=11.000000pt]t. Combine these constraints into a lfetime budetconstraint of this individual.
  
                                                 
•                                                         Restrict attention to a stationary solution in which each generation would consume the samefraction of its endowment when young. Write down the conditions that represents the clearingof the money market in an arbitrary period [size=11.000000pt]t. Use condition to find the real rate of return offiat money in a monetary equilibrium. Explain the path over time of the value of fiat money.
  
                                                 
•                                                         Find the Golden Rule allocation for this economy.
  
                                                 
•                                                         Find the optimal ([size=11.000000pt]c[size=8.000000pt]∗[size=8.000000pt]1[size=8.000000pt]t[size=11.000000pt],c[size=8.000000pt]∗[size=8.000000pt]2[size=8.000000pt],t[size=8.000000pt]+1). Compare it with the Golden Rule allocation found above.
  
  
  
                                         

                               
                       
               

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关键词：宏观经济 Constraints Generations Preferences equilibrium individual generation represent amount budget

Suppose n = 1. Suppose the endowment grows, i.e. ωt = (yt, 0) where yt = Ayt−1, and A > 1 is a constant. Also, ω1 = (y,0). There is a constant amount of fiat money M. Suppose the preferences
of generations 1, 2, ..., are and those of the IO are
u(c1, c2) = √c1 + √c2, uIO(c2) = c2.
1

a. Write down equations that represent the budget constraints in the first and second period of a typical individual from generation t. Combine these constraints into a lfetime budet constraint of this individual.
b. Restrict attention to a stationary solution in which each generation would consume the same fraction of its endowment when young. Write down the conditions that represents the clearing of the money market in an arbitrary period t. Use condition to find the real rate of return of fiat money in a monetary equilibrium. Explain the path over time of the value of fiat money.
c. Find the Golden Rule allocation for this economy.
d. Find the optimal (c∗1t,c∗2,t+1). Compare it with the Golden Rule allocation found above.

Suppose n = 1. Suppose the endowment grows, i.e. ωt = (yt, 0) where yt = Ayt−1, and A > 1 is a constant. Also, ω1 = (y,0). There is a constant amount of fiat money M. Suppose the preferences
of generations 1, 2, ..., are and those of the IO are
u(c1, c2) = √c1 + √c2, uIO(c2) = c2.

a. Write down equations that represent the budget constraints in the first and second period of a typical individual from generation t. Combine these constraints into a lfetime budet constraint of this individual.
b. Restrict attention to a stationary solution in which each generation would consume the same fraction of its endowment when young. Write down the conditions that represents the clearing of the money market in an arbitrary period t. Use condition to find the real rate of return of fiat money in a monetary equilibrium. Explain the path over time of the value of fiat money.
c. Find the Golden Rule allocation for this economy.
d. Find the optimal (c∗1t,c∗2,t+1). Compare it with the Golden Rule allocation found above.