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Consider a two period model. An agent gains utility from consumption today (c 1) and in the future (c2) according to U(c1, c2), that satisfied the...

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 < b < 1. Find the consumption function for c1 and the savings function.
2. Suppose the person lives for two periods, U = u(c1) + bu(c2), and can acquire an asset at price q, with c1 = w1 – qa and c2 = (d + q*)a + w2, where d = dividend and q* = selling price.
A. Find the first order conditions.
B. Find the asset demand function for a when utility takes the log form, as in 1B above.
HW assignment (Due Wed) 1. Consider a two period model. An agent gains utility from consumption today (c 1 ) and in the future (c 2 ) according to U(c 1 , c 2 ), that satisfied the usual assumptions. The budget constraints are c 1 = w 1 + s and c 2 = w 2 + (1+r)s, where w t 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(c 1 ) + blog(c 2 ), for 0 < b < 1. Find the consumption function for c 1 and the savings function. 2. Suppose the person lives for two periods, U = u(c 1 ) + bu(c 2 ), and can acquire an asset at price q, with c 1 = w 1 – qa and c 2 = (d + q*)a + w 2 , where d = dividend and q* = selling price. A. Find the first order conditions. B. Find the asset demand function for a when utility takes the log form, as in 1B above.
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