the only quantities of good 1 that Barbie can buy are 1 unit or zero units.For x₁ equal to zero or 1 and for all positive values of x₂, suppose that Barbie's preferences were represented by the utility function (x₁  6) (x₂  8) .Then if her income were $20, her reservation price for good 1 would be

A) $4.50.
B) $.75.
C) $8.
D) $4.
E) $1.23.

Question

Jaidan Twells · Accepted Answer

Final Answer : D, Explanation :  To find the reservation price for good 1, we need to find the maximum price that Barbie is willing to pay for one unit of good 1. We can find this by setting her utility of purchasing one unit equal to her utility of purchasing zero units:(x 1     6) = (0 2     8)Simplifying this equation, we get:   6 + x 1     6 =    8x 1     6 =    8 -    6x 1  = 2Now, we can find the maximum price that Barbie is willing to pay for one unit of good 1 by dividing her income ($20) by the quantity she is willing to purchase (1):Reservation price for good 1 = $20/1 = $20However, since she is only willing to pay a maximum of $2 for good 1, her reservation price is actually $2 or less. The closest answer choice to this is D) $4.

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