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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- a. List and briefly explain the main assumptions we make on consumer preferences.b. For each assumption, provide an example consumer preference that does not satisfy the assumption (you may illustrate your answers by using a graph).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).4. If we have the utility function, U(x)=(x−7)^2, and we know that there is an indifference set around x = 4 and an upper contour set of x = 6. How to graphically represent this function? I'm confused about how to draw the upper contour set on the graph? I know the concept that upper contour is the area over the convex line, but don't know how to put it on the graph. Could you draw a simple graph to help me identify the upper contour?
- Consider that there are two goods, good X and good Y. a) Give the definition of "indifference curve" (briefly in one sentence). b) Is it possible for two indifference curves to intersect at a certain consumption bundle in (X,Y) plane? If yes, explain and give an example. If not, explain and provide a reason for why it is not possible.1. Is it impossible for two indifference curves to intersect one another? why? 2. What does it mean that preferences are complete? Now would the real-life implica- tions of this assumption look like?Suppose that Jones and Smith have each decided to allocate $1000 per year to an entertainment budget in the form of hockey games or rock concerts. They both like hockey games and rock concerts and will choose to consume positive quantities of both goods. However, they differ substantially in their preferences for these two forms of entertainment. Jones prefers hockey games to rock concerts, while Smith prefers rock concerts to hockey games. a. Draw a set of indifference curves for Jones and a second set for Smith. b. Using the concept of marginal rate of substitution, explain why the two sets of curves are different from each other.
- Another instance when people are likely not to spend a dime (or a minute) on an item is when they have a dislike for mixing the item with other items available. In this case, we say the consumer has ‘non-convex preferences’ and indifference curves are bowed out from the origin. In plain language, the consumer has a preference for binging. We often feel this way towards our favorite social media app. Consider a kid who has four hours a day to spend on social media. They enjoy spending time on Snapchat (x) or spending time on Twitter (y). a) Write the kid’s time constraint and illustrate it in a graph where you measure time spent on Snapchat along the horizontal axis and time spent on Twitter along the vertical axis. This kid’s utility from time spent on Snapchat and time spent on Twitter is U(x,y) = 4x2+ y2. b) In your graph, draw a couple of the kid’s indifference curves. Notice how the kid’s |MRSY,X| increases along each curve as he spends more time on Snapchat and less time on…1) Consider an indifference map which consists of vertical lines. What can you say about the consumer's preferences for these two goods? 2) How will the indifference map of this consumer change if the two goods are interchanged on the two axes? (That is, good earlier on the x-axis is moved to y-axis and good earlier on the y-axis is moved to x-axis.)Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.
- Suppose you have an income of $24 and the only two goods you consume are apples (x1) and peaches (x2). The price of apples is $4 and the price of peaches is $3. Suppose that your optimal consumption is 4 peaches and 3 apples. a. Illustrate this in a graph using indifference curves and budget lines. b. Now suppose that the price of apples falls to $2 and I take enough money away from you to make you as happy as you were originally. Will you buy more or fewer peaches? Provide a graphical representation.Draw YOUR indifference curve for the consumption of two goods (you pick the goods – be creative!) Make sure to include labels. Why did you choose these two goods? Why do you view these as being a tradeoff? Carefully explain why the indifference curve has the shape you created. (Hint: Discuss the slope. What it means and how it changes) Determine a budget that will be allocated towards your consumption of these two goods. Given the budget, prices for the goods, and your preferences, how will you find the utility-maximizing combination? Give an intuitive answer as well as a graphical answer (make sure to label the graph accordingly).Suppose that you are thinking about joining COSTCO. You must pay a membership fee, but once you joined you can buy products at a lower price. Assume you would buy only one good, say, paper towels at COSTCO. After careful consideration you think that you are indifferent between joining and not joining COSTCO. Illustrate your dilemma with a graph that includes two budget lines (with or without COSTCO) and an indifference curve. Make sure that you labelled the axes and all the shapes in your graph.