Question: Time is indexed byt{1, 2}. Utility for each agent or consumer is U(c1,c2) = lnc1+lnc2,0 < <1. The endowment for the agent is (y1,y2) =

Time is indexed byt{1, 2}. Utility for each agent or consumer is

U(c1,c2) = lnc1+lnc2,0< <1.

The endowment for the agent is

(y1,y2) = (3, 33) .

An agent maximizes utility subject to the lifetime budget constraint c1+c21 +r1=y1+y21 +r1.How much does the agent save in the first period? Use the following parameter

= 1/2

r1= 1/10.

2. Time is indexed byt {1, 2}. Agents are indexed by i {A,B}. There are NAtype-Aagents. There are NBtype-Bagents. Utility for both agents is

U9ci1,ci2)= lnci1+lnci2,0< <1.

The endowments for the two types of agents are (yA1,yA2)= (x, 0) (yB1,yB2)= (0,z) .

Agents maximize utility subject to the lifetime budget constraint

ci1+ci21 +r1=yi1+yi21 +r1.

The economy has the following values for parameters:

N^a=N^B=1,000

x=1.0

z=1.07x

=0.9

What is the equilibrium interest rate r1?

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