Asked by Lupita Sanchez on Jun 18, 2024
Verified
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.
Reservation Price
The highest price a consumer is willing to pay for a good or service, beyond which they would choose not to make a purchase.
Barbie's Preferences
A hypothetical concept referring to the assumed tastes or choices that the iconic doll character "Barbie" might have, based on her lifestyle and marketed products.
Good 1
A term used in economic models to represent the first of multiple goods considered in analysis, often with unspecified characteristics.
- Absorb the fundamentals of demand functions and how to read them effectively.
- Ascertain the reservation prices considering different consumer tastes and financial statuses.
Verified Answer
SC
Sapna ChandanJun 21, 2024
Final Answer :
A
Explanation :
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 6)(x2 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.
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.
Learning Objectives
- Absorb the fundamentals of demand functions and how to read them effectively.
- Ascertain the reservation prices considering different consumer tastes and financial statuses.