Question

ds/ECN100 Practice_Wk2,ConsumerMaxProblem.pdf Courses DocsHulu Xfinity Stream SHOWTIME H Netflix FAFSA My Sessions ECN100 PRACTICE PROBLEM FOR WEEK 2 Question: Consider the utility function y. (a) Make a table of 4 (x, y) consumption bundles that all yield a utility of 4 (b) Plot the four points on a graph with x on the x-axis and y on the y-axis. Draw a smooth line combining the points. (c) what is the marginal utility of x? what is the marginal utility of y? (d) Make a plot of the marginal utility of x. Does this utility function exhibit diminishing marginal utility for x? Anupgne sn pres or th tre gods e) What is MRSs,? What does it represent? (f) If for a given bundle (x,y) we have that MRSryメn, why do we know this bundle must (2) Use MRSy to find the optimality condition (Le. what must be true for any utility (Ch) Of course there are many (x,y) bundles that can satisfy this condition, and the consumer not be maximizing the utility of the consumer? maximizing bundle). would prefer to have an infinite amount of both x and y. Unfortunately, the consumer has a budget constraint. What is it? 0) Use the budget constraint to solve for the consumer's optimal consumption bundle. MacBook Air

Answer 1

U = x^0.5y

(a)

When U = 4, following (x, y) bundles will yield an utility of 4:

(x, y) = (1, 4), (4, 2), (16, 1) and (64, 0.5).

(b)

(c)

MUx = $\dpi{80} \partial$ U/$\dpi{80} \partial$x = (0.5y) / (x^0.5)

MUy = $\dpi{80} \partial$ U/$\dpi{80} \partial$y = x^0.5

(d)

Holding y constant, as x increases, (x^0.5) increases, so MUx decreases, indicating diminishing MUx.

The MUx curve is as follows.

NOTE: As per Answering Policy, 1st 4 parts are answered.