Question

Alice has utility function ?(?1, ?2) = min⁡{?1, 2?2}. The interest rate is 5%. Her income in Period 1 is $1000 and her income in Period 2 is 1100.

1. a) Write down the optimality condition that must hold for Alice at her optimal consumption.

2. b) Find Alice’s optimal consumption choices (her optimal values of ?1 and ?2)

3. c) Is Alice a borrower or a lender? Explain.

Answer 1

Ans. Utility function, U = Min{c1, 2c2}

a) This is a function showing that the consumption in period 1 and 2 are perfect complements. So, the consumption in period 1 must be double that of consumption in period 2.

So, c1 = 2c2 ---> Eq1

b) Alice's budget constraint,

c1 + c2/(1+0.05) = 1000 + 1100/(1+0.05)

=> 1.05c1 + c2 = 2150

Substituting Eq1 in the budget constraint, we get,

1.05*2c2 + c2 = 2150

=> c2 = $693.5483

Thus, from Eq1,

c1 = $1387.0967

c) As consumption in period 1 is more than the income, so, Alice is a borrower and borrows $387.0967 in period 1 for consumption.

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