Sandra’s utility function is U(x,y) = x + 2y - y. If we draw her indifference curves with x on the horizontal axis, and y on the vertical axis, then these indifference curves are everywhere downward sloping and get flatter as one moves from left to right. is this ture or false?
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Sandra’s utility function is U(x,y) = x + 2y - y. If we draw her indifference
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- Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. Where x₁ measures the number of episodes watched of Show 1 and x2 measures the number of episodes watched of Show 2, Jeff's preferences can be represented by u(x₁, x2 ) = x² + ax². Jeff has 13 hours available for watching Netflix today. Each episode of Show 1 lasts — hours, while each episode of Show 2 lasts 1 hour. Draw an indifference curve for Jeff, then answer the following questions. If rounding is needed, please round to 3 decimal places. a) When a = 2, Jeff optimally watches episodes of Show 1..... (fill in the blank) b) ... and he watches episodes of Show 2. (fill in the blank) c) When a = 6, Jeff optimally watches episodes of Show 1..... (fill in the blank) d) ... and he watches episodes of Show 2. (fill in the blank)Could Figure 3.2 be a single indifference curve if preferences are monotonic?
- Explain why two indifference curves cannot intersect.Define A consumer prefers a higher indifference curve to a lower one.We claimed in the text that if preferences were monotonic, then a diag-onal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)
- There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. Where x₁ measures the number of episodes watched of Show 1 and x2 measures the number of episodes watched of Show 2, Jeff's preferences can be represented by u(x₁, x₂) = x² + ax. Jeff has 8 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. Draw an indifference curve for Jeff, then answer the following questions. If rounding is needed, please round to 3 decimal places. a) When a = 2, Jeff optimally watches_ episodes of Show 1..... (fill in the blank) b)... and he watches episodes of Show 2. (fill in the blank) c) When a = 6, Jeff optimally watches_ episodes of Show 1..... (fill in the blank) d) ... and he watches. episodes of Show 2. (fill in the blank)For each of the following utility functions draw the indifference curve that passes through (1,1). Label at least three points on each curve and indicate the direction of increased preference: a) u(x1, x2 ) = 3x1 b) u(x1, x2 ) = x1 + 2x2 c) u(x1, x2 ) = x1+ logx2 d) u(x1, x2 ) = min (2x1, x2) e) u(x1, х2) %3D max (1, x2)Harry's indifference curve for popcorn (X1) and butter (X2) is U-min(X1, 3X2). Sketch two indifference curves. Make sure your axes and intercepts are labeled. True or False and explain: Perfect Substitute utility functions exhibit zero marginal rate of substitution True or False and explain: If a consumer's indifference curve is given by x2= 50/x1, this consumer is indifferent between the two bundles (100, 2) and (5, 10)
- Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D,F)= 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane's annual travel budget is $4000. An indifference curve associated with a level of utility equal to 800 and an indifference curve associated with utility of 1200 are illustrated in the figure to the right. Using the line drawing tool, graph Jane's budget line. Label this line L,. Carefully follow the instructions above, and only draw the required object. Can Jane afford any of the bundles that give her a utility of 800? Can Jane afford any of the utility bundles that give her a utility of 1200? Find Jane's utility-maximizing choice of days spent traveling domestically and days spent in a foreign country. days of domestic travel and days of foreign travel. (Enter…3.1 Graph a typical indifference curve for the following utility functions, and determine whether they have convex indifference curves (i.e., whether the MRS declines as x increases). a. U(x, y) = 3x + y. b. U(x, y) = √x. y. c. U(x, y) = √x + y. d. U(x, y) = √x² - y². xy e. U(x, y): x + yLucy's company has just promoted her to a managerial position and given her a new office. She is very fond of small Persian carpets and Native American paintings and wants to get some carpets and paintings for her office. Her utility function for carpets (x) and paintings (y) is given by Using Excel's charting tool, draw an indifference curve for U = 4 and another one for U = 6, where both indifference curves contain 1, 2, 4, and 8 carpets on a graph, with carpets on the horizontal axis and paintings on the vertical axis. As described in Exercise 8.1, Lucy wants carpets and paintings for here office. Her company has given her a budget of $7200 for this purpose. Persian carpets of the size that she wants can be purchased for $900 each and paintings from a local Native American artist cost $400 each. Using Excel's charting tool, draw Lucy's budget constraint if her budget is $5000. Use 0, 1, 2, 3, and 5 carpets as possible quantities. Put carpets on the…
