Xavier and Yvette Are the Only Two Persons on a Desert

question 1

Multiple Choice

Xavier and Yvette are the only two persons on a desert island. There are only two goods, nuts and berries. Xavier's utility function is U(N_x, B_x) = N_xB_x. Yvette's utility function is U(N_y, B_y) = 2N_y + B_y. Xavier is endowed with 3 units of berries and 8 units of nuts. Yvette is endowed with 6 units of berries and 8 units of nuts. In a competitive equilibrium for this economy, how many units of berries does Xavier consume?

• A) 12.50
• B) 19
• C) 7.50
• D) 9.50
• E) None of the above.

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Definitions:

Internal Rate of Return

A financial metric used to estimate the profitability of potential investments, calculating the discount rate that makes the net present value of all cash flows from the investment equal to zero.

Present Value

The present value of a future amount of money or a series of cash flows, calculated using a given interest rate.

Annuity

A finance-related product designed to issue a predetermined series of payouts to an individual, typically aimed at serving as an income source for retirement.

Net Present Value

A calculation that compares the present value of cash inflows to the present value of cash outflows over a period of time, used in capital budgeting to assess profitability of investments.