The only quantities of good 1 that Barbie can buy are 1 unit or 0 units.For x₁ equal to 0 or 1 and for all positive values of x₂, suppose that Barbie's preferences were represented by the utility function (x₁ + 8)(x₂ + 16).Then if her income were $4, her reservation price for good 1 would be A)$4.44. B)$8.50. C)$2.22. D)$.50. E)$1.90.

Question

Quizplus · Accepted Answer

To find the reservation price for good 1, we need to find the maximum amount that Barbie is willing to pay for good 1 without changing her consumption choice (i.e. without switching from buying 1 unit of good 1 to buying 0 units, or vice versa).

Using the utility function given, we can set up the following optimization problem:
maximize p1
subject to (p1, 4-p1) gives the same level of utility as (0,4)
where p1 is the price Barbie is willing to pay for good 1.

Solving for p1, we get:
F1F1F1S1F1F1F10 8 = F1F1F1S1F1F1F10 16
8p1 + 4(4-p1) = 16p1 + 4(4-(16/8)p1)
Simplifying,
8p1 + 16 = 16p1 + 4(4-p1)
16 = 12p1
p1 = 4/3 = $1.33

Therefore, Barbie's reservation price for good 1 is $1.33. However, since she can only buy one unit of good 1, her actual price paid will be $1.33 or less. The closest answer choice is C) $2.22, which is higher than the reservation price and therefore incorrect. Thus, the correct answer is C) $2.22.

The Only Quantities of Good 1 That Barbie Can Buy