Patience Has the Utility Function U(c₁, C₂)=c^1/2₁ +2c^1/2₂ Where C₁

question 46

Essay

Patience has the utility function U(c₁, c₂)=c^1/2₁ +2c^1/2₂ where c₁ is her consumption in period 1 and c₁ is her consumption in period 2.She will earn 100 units of the consumption good in period 1 and 100 units of the consumption good in period 2.She can borrow or lend at an interest rate of 10%.
a.Write an equation that describes Patience's budget.
b.If Patience neither borrows nor lends, what will be her marginal rate of substitution between current and future consumption?
c.If Patience does the optimal amount of borrowing or saving, what will be the ratio of her period 2 consumption to her period 1 consumption?

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Definitions:

Bailee

A person or entity who is given temporary possession but not ownership of a property or goods under a bailment agreement.

Deteriorate

To become worse or diminish in quality, value, or strength.

Public Property

Assets owned by governmental entities that are meant for public use and benefit, such as parks, roads, and public buildings.

Government

is the system or group of people governing an organized community, generally a state, setting policies and exercising executive power.