Clarissa’s utility function is U(r, z) =z + 160r r^2, where r is the number of r
ID: 3121675 • Letter: C
Question
Clarissa’s utility function is U(r, z) =z + 160r r^2, where r is the number of rose plants she has in her garden and z is the number of zinnias. She has 250 square feet to allocate to roses and zinnias. Roses each take up 4 square feet and zinnias each take up 1 square foot. She gets the plants for free from a generous friend. If she acquires another 100 square feet of land for her garden and her utility function remains unchanged, she will plan
A)25 more roses and no more zinnias.
B)20 more roses and 20 more zinnias.
C)max(1, min(99, z+100)) more zinnias and some more roses.
D)100 more zinnias and no more roses.
A)25 more roses and no more zinnias.
Explanation / Answer
The MRS of given utility function = 160 - 2*r (by differentiation)
Clarissa for interior solution will try to maximize her utility by
MRS = P1/P2 ..........(1)
P1/P2 = 4
=> 160-2r = 4
=> r = 156/2 =78.
Since r is a constant, the number of roses will remain the same.
Thus upon adding more land, she will not add any roses.
All the additional area i.e 100 sq ft will be for planting zenias. Since each zenia takes 1 sq ft, total zenias planted will be 100.
So the answer is D. 100 more zenias and no more roses.