a. List and briefly explain the main assumptions we make on consumer preferences (one sentence of explanation for each). b. For each assumption, provide an example consumer preference that does not satisfy the assumption (you may illustrate your answers by drawing graphs).
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- J 4 True or false? Be sure to explain your answer in detail. Suppose the utility function u(x1, x2) = 2x1x2 represents a consumer's preferences. Then the utility function v(x1,x2) = x1x2 also represents the same consumer's preferencesUse the Law of Diminishing Marginal Utility to discuss why Market Demand has to have a downward slope. In other words, in order for consumers to demand a higher quantity of an item, its price must fall. Also use the Law of Diminishing Marginal Utility to explain why consumers often prefer to purchase a variety of goods and services (in other words, we are unlikely to fill a grocery cart with many units of the exact same product). Finally, use the utility optimizing condition that the ratio of Marginal Utility to Price for any good has to be the same across all goods to justify why it may be rational behavior to buy an item that is expensive compared to other items. Discuss these concepts using examples from your own experience and observations.What is the difference between ordinal utility and cardinal utility? Explain why the assumption of cardinal utility is not needed in order to rank consumer choices!
- The following graphs show two indifference curves, a brown one and a blue one, where blue is more useful than brown, and the direction in which the person's utility increases (red arrow). Assume that all of this person's indifference curves maintain the same shape and that the direction of increase in utility in each is the same. Answer the following 4 questions: - In Graph 1, the utility function that represents the preferences of the person ____ (is strictly monotonous and weakly quasi-concave / not monotonous and strictly quasi-concave / is strictly monotonous and is not quasi-concave/ it is strictly monotonous and strictly quasi-concave) - In graph 2, the utility function that represents the person's preferences ______ (is weakly monotonous and is not quasi-concave / not monotonous and not quasi-concave / strictly monotonous and is not quasi-concave / not monotonous and weakly quasi-concave) - In graph 3, the utility function that represents the person's preferences ______( none of…Complete the following table and answer the questions below: Units Consumed Total Utility Marginal Utility 0 0 — 1 10 10 2 8 3 25 4 30 5 3 6 34 a. At which rate is total utility increasing: a constant rate, a decreasing rate, or an increasing rate? How do you know? b. True or False. “A rational consumer will purchase only 1 unit of the product represented by these data, because that amount maximizes marginal utility.” c. True or False. “It is possible that a rational consumer will not purchase any units of the product represented by these data.”I need help with this question in my homework. Suppose a consumer’s utility function is given by U(X,Y) = MIN (5X, Y). Also, the consumer has $60 to spend, and the price of good X is P(x) = $5. Let good Y be a composite good (good Y is the “numeraire”) whose price is P(y) = $1. So, on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. What is the Indirect Utility Function? What is the Expenditure Function?