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The question is:
In each of the following examples, a consumer purchases just two goods: x and y. Based on the information in each of the following parts, sketch a plausible set of indifference curves (that is, draw at least two curves on a set of labeled axes, and indicate the direction of higher utility). Also, writedown a utility function u(x, y) consistent with your graph. Note that although all these preferences should be assumed to be complete and transitive (as required for utility representation), not all will be monotone.
(a) Jessica enjoys bagels x and coffee y, and consuming more of one makes consuming the other more enjoyable.
(b) Plamen loves mocha swirl ice cream x, but he hates mushrooms y.
(c) Jennifer likes Cheerios x, and neither likes nor dislikes Frosted Flakes y.
(d) Edward always buys three white tank tops x for every pair of jeans y.
(e) Nancy likes both peanut butter x and jelly y, and always gets the same additional satisfaction from an ounce of peanut butter as she does from two ounces of jelly.
Step-by-step explanation:
The utility functions consistent with the graphs are:
(a) u(x, y) = xy
(b) u(x, y) = x - y
(c) u(x, y) = x
(d) u(x, y) = min(x, 3y)
See attachments for the graphs.
Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:
The identity that relates the sine squared and the cosine squared of the angle, as follows:
In this problem, we have that the sine is given by:
Hence, applying the identity, the cosine is given as follows:
The tangent is given by the sine divided by the cosine, hence:
More can be learned about trigonometric identities at brainly.com/question/24496175
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