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:

Profit Margin

The percentage of revenue that remains as profit after all expenses have been subtracted from sales.

Investment Turnover

Investment turnover measures the rate at which a company or fund buys and sells its portfolio of investments, helping to understand its trading activity level and potential profitability.

Investment Center Performance

A measure of the efficiency and profitability of an investment center, which is a business unit responsible for its own revenues, expenses, and assets.

Operating Income

The profit earned from a firm's core business operations, excluding deductions from interest and taxes.