1 consider a two period model an agent gains utility from

Reference no: EM13374445

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.

Reference no: EM13374445

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