1. Consider a two-period model. An agent gains utility from consumption today (c1) and in the future...

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1. Consider a two-period model. An agent gains utility from consumption today (c1) and in the future (c2) according to U(c1, c2), that satisfied the usual assumptions. The budget constraints are c1 = w1 + s and c2 = w2 + (1+r)s, where wt is labor income in period t, s is savings, and r is the interest rate. A. Set up the decision problem and find the first order conditions. B. Suppose U = log(c1) + blog(c2), for 0 
	
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1. Consider a two period model. An agent gains utility from consumption today (c ) 
1
and in the future (c ) according to U(c , c ), that satisfied the usual assumptions. The 
2 1 2
budget constraints are c = w + s and c = w + (1+r)s, where w is labor income in 
 XXXXXXXXXXt
period t, s is savings, and r is the interest rate.  
 A. Set up the decision problem and find the first order conditions. 
 B. Suppose U = log(c ) + blog(c ), for 0

Robert · Accepted Answer

1. Note we have corrected the errata c1=w1-s instead of +. In a 2 period model, we 
are treating s as savings, not as initial endowmeent! 
a. The Optimisation problem can be written as 
maxc1,c2 U(c1,c2) 
subject to: (w1-c1)(1+r) – c2+w2=0 
Set up the Lagrangean, 
L= U(c1,c2)-λ*{(w1-c1)(1+r) – c2+w2} 
Assuming Q is continuously differentialble,

1. Consider a two-period model. An agent gains utility from consumption today (c1) and in the future (c2) according to U(c1, c2), that satisfied the usual assumptions. The budget constraints are c1 =...

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