# doubt

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## doubt

 6.15 Clarissa's utility function is U(r; z) = z + 80r-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: (a) plant 100 more zinnias and no more roses. (b) plant 25 more roses and no more zinnias. (c) plant 99 more zinnias and some more roses. (d) plant 20 more roses and 20 more zinnias. (e) do none of the above.
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## Re: doubt

 Plant no more roses, i.e. option a MRS of given utility function is 80-2r So, user for interior solution will try to maximize his utility by MRS = P1/P2                     ..........(1) P1/P2 = 4 while P1/P2 is constant, hence the MRS. Thus r will be a constant ,i.e 42 roses when you solve eq 1  such that utility can be maximized. Thus upon adding more land, he will not change his consumption of roses. While, on a close look, u will see its a quasi-linear preference i.e. U(z,r) = z+80r-r^2 = k Z= k - v(r) hence no change in consumption of r upon addition of more income(land here).
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## Re: doubt

 but ans is c i also did same