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:

Indeterminate

A term used in various contexts to describe situations, outcomes, or mathematical expressions that cannot be definitively resolved or calculated.

Ice Cream Cone

A sweet, edible cone filled with ice cream, served as a dessert or snack.

Demand Curve

A graphical representation illustrating the relationship between product price and the quantity of the product demanded.

Indifference Curves

Graphical representations of different bundles of goods between which a consumer is indifferent, showing the same level of satisfaction or utility from each bundle.