Question 1: Consider a consumer who lives for two periods. The first period income is m₁, the

second period income is m₂. Denote the consumer's consumption in the first period and

second period by c₁, c₂, respectively. The consumer's preferences are given by \(\sqrt{{{c}_{1}}}+\delta \sqrt{{{c}_{2}}}\).

a. Write down the consumer's choice problem.

b. Derive the first order condition and characterize the solution.

c. What is the solution to the problem if \(\delta \) = 0? What is the solution if \(\delta \) = 1? explain.

d. For general 0 < \(\delta \) < 1, is it possible that the consumer's consumption in each period is the same (that it, the solution is \(c_{1}^{*}=c_{2}^{*}\) )? If it is, find the conditions under

which this is the solution.

Question 2: Repeat question 1 when the preferences are given by \({{c}_{1}}+\delta {{c}_{2}}\).

Question 3: Consider preferences described by \(U\left( {{x}_{1}},{{x}_{2}} \right)=\min \left\{ 4{{x}_{1}},{{x}_{2}} \right\}\).

a. Depict a typical indifference curve.

b. Suppose the income and prices are: m = 10 and p₁ = p₂ = 1. Can the bundle

x₁ = 5, x₂ = 5 solve the consumer's choice problem given the preferences above? Explain

(without solving the problem).

c. Find the solution to the consumer's choice problem (for general income and

Price: $28.95

Solution: The downloadable solution consists of 7 pages, and 486 words
Deliverable: Word Document and pdf