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Question: 1 consider the following utility functions a for each of...

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1. Consider the following utility functions (a) For each of these utility functions: i. Find the marginal utility of each good. Are the preferences mono- tone? ii. Find the marginal rate of substitution (MRS) iii. Define an indifference curve. Show that each indifference curve (for some positive level of utility) is decreasing and convex. (b) For the utility function u2(x1, x2), can you find another utility function that represents the same preferences? Find the relevant monotone trans formation f(u) (c) Repeat questions 1(aii and 1(a)iii for the function u3(x1, x2)min 2, 2

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