4. a. Consider a consumer with preferences defined over x and y. Demonstrate that it is possible they would choose to consume some of both commodities when their income is I but would choose to consume only x when their income is I’ > I. (Remember: if you can draw it without violating any of the basic assumptions on preferences, it could happen.) b. Conversely, demonstrate that it is possible they would choose to consume only x when their income is I but would choose to consume x and y when their income is I’ > I. c. Finally, show it is possible that they would choose to consume only y when their income is I but would choose to consume only x when their income is I’ > I.

4. a. Consider a consumer with preferences defined over x and y. Demonstrate that it is possible they would choose to consume some of both commodities when their income is I but would choose to consume only x when their income is I’ > I. (Remember: if you can draw it without violating any of the basic assumptions on preferences, it could happen.) b. Conversely, demonstrate that it is possible they would choose to consume only x when their income is I but would choose to consume x and y when their income is I’ > I. c. Finally, show it is possible that they would choose to consume only y when their income is I but would choose to consume only x when their income is I’ > I.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.9P

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4. a. Consider a consumer with preferences defined over x and y. Demonstrate that it is possible theywould choose to consume some of both commodities when their income is I but would choose toconsume only x when their income is I’ > I. (Remember: if you can draw it without violating anyof the basic assumptions on preferences, it could happen.) b. Conversely, demonstrate that it is possible they would choose to consume only x when theirincome is I but would choose to consume x and y when their income is I’ > I.c. Finally, show it is possible that they would choose to consume only y when their income is I butwould choose to consume only x when their income is I’ > I.
. Consider a consumer with preferences defined over x and y. Demonstrate that it is possible theywould choose to consume some of both commodities when their income is I but would choose toconsume only x when their income is I’ > I. (Remember: if you can draw it without violating anyof the basic assumptions on preferences, it could happen.)
2. What does it mean that preferences are complete? Now would the real-life implica- tions of this assumption look like?
Answer the following short questions:a. Suppose that a consumer’s preferences between goods x andy are represented by the utility function u(x, y) = x^2 + 16xy + 64y^2. If these two goods have the same price, describe the optimal consumptionchoice of this consumer.b. Suppose that when the price of a good change, the incomeand substitution effects change the consumer’s demand for that goodin opposite directions.i. Is this good a normal or an inferior good? Explain.ii. Is this good a Giffen or an ordinary good? Explain.c. Is the following statement true or false? The differencebetween a monopolist’s marginal cost and its profit-maximizing price issmaller when the demand is more elastic.
If the preferences are concave will the consumer ever consume both ofthe goods together?
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1. Say that there are two goods in the world, books and video games. Say that we observed two of Jim's choices: he chooses bundle A from the budget set bounded by budget line 1, and the bundle B from the budget set bounded by budget line 2. video games B A budget line 2 budget line 1 books a) For each of the two goods, based on the diagram: is the good normal, inferior, or we can't say for sure? Is the good ordinary, Giffen, or we can't say for sure? Explain. b) For which of the two budget lines is the opportunity cost of a book higher and why? What does that statement mean in the context of this model?
Suppose the seventh carrot you consume provides a marginal utility of 1 util and after eating the eighth carrot, you would have a total of 5 utils. If you consume the eighth carrot your marginal utility will O decrease by 4 O increase by 4 decrease by 1 increase by 1 O not enough information to determine the answer.
Let the following table represent the total utility of a given consumer,In the cardinal utility approach. A) Calculate the MUx and MUy and fill the table in the 4th and 5th rows. B) If the two products (X&Y) are free goods how many of X and Y should the cons consumer take to maximize utility? C) What is the maximum utility of X and Y if they are free?. D) Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? E) What is the total utility of X and Y? F) Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility? G) What are the total utility of X and Y
Martha spends 5 hours of free time exercising and playing music per day. The table below represents the level of utility she receives from the various combinations of exercise and music activities. For instance, if she only plays music, her total utility from exercise will be 0, and the utility from music will be 50. If she exercises for 1 hour, she will receive a level of utility of 25. Utility is measured in 'utils'; those numbers are arbitrary and designed to quantify the benefits received from various actions. Utility Utility from from Exercise Music 50 utils from 5 hours of O utils from O hours of exercise music 25 utils for 1 hours of exercise 45 utils from 4 hours of music 40 35 45 20 50 The utility patterns in the table illustrate the law of marginal diminishing utility because... LO
If we observe that a consumerâ s budget constraint has shifted inward, we can assume that the consumer will buy O fewer normal goods and fewer inferior goods O more normal goods and more inferior goods O fewer normal goods and more inferior goods more normal goods and fewer inferior goods