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 + 4).Then if her income were $16, her reservation price for good 1 would be A)$2.86. B)$2.50. C)$5.71. D)$1.50. E)$.57.

Question

Quizplus · Accepted Answer

To find Barbie's reservation price for good 1, we need to find the maximum amount she is willing to pay for it. We know that her utility function is (x₁ F1F1F1S1F1F1F10 6)(x₂ F1F1F1S1F1F1F10 4). Using the budget constraint, we can set up the equation: $16 = p1q1, where p1 is the price of good 1 and q1 is the quantity of good 1. We can then solve for q1 in terms of p1: q1 = 16/p1. Substituting q1 into the utility function, we have U = (16/p1)6 + (16/p2)4. To find the maximum reservation price, we need to take the derivative of U with respect to p1 and set it equal to 0: dU/dp1 = -96/p1^2 = 0. Solving for p1, we get p1 = $2.86. Therefore, Barbie's reservation price for good 1 is $2.86. She is willing to pay up to $2.86 for one unit of good 1 without decreasing her utility.

The Only Quantities of Good 1 That Barbie Can Buy