Jean-Pierre has preferences represented by the utility function U( x, y) = min{ 2 x + y, x + 6 y}. If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (7, 7)? a.–2 b.–7/7 c.–1/2 d.–1/6 e.–6/2
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Jean-Pierre has preferences represented by the utility function U( x, y) = min{ 2 x + y, x + 6 y}. If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (7, 7)?
a.–2
b.–7/7
c.–1/2
d.–1/6
e.–6/2
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- Take Jeremys total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremys utility.Page of 3 > Due November 1, 2 Press Esc to exit full screen A. Jack enjoys a cup of cappuccino every morning, which is made with equal parts of steamed milk (m) and espresso(e). Suppose Jack's utility function U(m, e) = min(m, e). Graph Jack's indifference curves when U = 4 and U = 8. B. Leslie buys 2 goods: z and y. His utility function is U(z,y) = 5x+3y. 1. Plot this consumer's indifference curves when U = 15 and U = 20. What is the shape of Leslie's indifference curves? 3. For Leslie, how are these two goods related? C. Leslie's friend Tim has a different utility function for the same goods U(x, y) = √zy. 1. Plot this consumer's indifference curves when U = 15 and Ū = 20. 2. What is the shape of Tim's indifference curves? D. A consumer's utility function for goods 2 and y is U(z,y) = x+2y. 2. 1. Calculate the consumer's marginal utility for each good at (2,2) (Hint: marginal utility represents the amount of utility the consumer gains by consuming one more unit of this good. You can…1. Doreen is looking for a flat to rent in Brighton. a. In choosing a flat, she cares about two characteristics: the number of bedrooms (x), and the number of bathrooms (y). Her utility function is U(x,y) = min(x, 2y). She has £1000 to spent on rent per month. The rental price per bedroom in Brighton is £400, and the price per bathroom is £200. (For example, a flat with three bedrooms and two bathrooms would rent for £1600 per month.) How many bedrooms and bathrooms does Doreen choose to rent optimally? b. Doreen now needs to furnish her flat. She has £500 to spend. However, she would also like to buy some clothes for her new job. The cost of furniture f is £50 per unit and the cost of clothing c is £20 per unit. Her utility function over furniture and clothing is U(f.c) = f0.3c0.7. How much does she spend in total on furniture, and on clothing? c. The local furniture shop runs a flash sale of 50% off, on all prices. How much does Doreen now spend on furniture, and on clothing?…
- 4.4 (0) Phil Rupp's utility function is U(x, y) = max{x, 2y}. (a) On the graph below, use blue ink to draw and label the line whose equation is x = 10. Also use blue ink to draw and label the line whose equation is 2y = 10. (b) If x = 10 and 2y < 10, then U(x, y) If x < 10 and 2y = 10, %3| then U(x, y) (c) Now use red ink to sketch in the indifference curve along which U (x, y) = 10. Does Phil have convex preferences?. 15 10 5 10 15 20 203. Sam has set aside $480 for entertainment this month, which is golf (x) and/or bowling (z). A round of golf is $40 and a night of bowling is $30. His utility function is U = 3x + 2z. What is his MRS? a. b. c. Solve for the optimal choice of golf and bowling. Draw a graph of the budget line (including intercepts), a few indifference curves, and the optimal choice for Sam.2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current in come is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?
- 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?Alex has a monthly budget of $72 to spend on commuter train trips and organic pasta. Each train trip costs $12; each box of pasta costs $6. Alex's preferences for train travel and pasta are represented by the indifference map on the following page. a. Determine which line (L1, L2, L*, or L**) represents Alex's budget constraint. b. Find their utility-maximizing bundle (E1, E2, e*, or e**). How many train trips will Alex take? Suppose the state government establishes a program to subsidize public transportation for commuters, such that each train trip now costs Alex $6. c. Determine which line (L1, L2, L*, or L**) represents Alex's new budget constraint. d. Find their new utility-maximizing bundle (E1, E2, e*, or e**). Determine how many train trips Alex will now take. e. Find the size and direction (positive or negative) of the substitution effect for train trips. As part of your answer, state the starting quantity and ending quantity of train trips that represent this effect. f. Find…2. Eren's two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V²M Last year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. a. b. C. Calculate the change in consumer surplus from consuming the expensive meals considering the price change (Hint: you need to compare his optimal consumption bundle before and after the price change to get the change in CS). Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV). Calculate for the equivalent variation (EV) for the price change.
- 3. 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 it intersected some indifference curve twice?)4 Emily goes camping on the weekend and eats marshmallows (M) and crackers (C) there. She wants to match 1 marshmallow with 2 crackers, but does not eat in different proportion (i.e., perfect com- plement). The price of a marshmallow is 10 cents and the price of a cracker is 5 cents, and she spend up to $3 in total. a) Write down a utility function which represents Emily's preferences over marshmallows and crackers. b) How many marshmallows and crackers is she going to consume? (Hint: the first-order conditions will not help; draw the budget constraint and the indifference curves and look at the highest one that intersect the budget constraint). c) What is the exact value of Emily's indirect utility?The table below represents how Marco feels about chocolate candy bars. a. Fill in the missing values for total utility and marginal utility. Instructions: Enter your answers as a whole number. Chocolate Candy Bars and Marco's Utility Chocolate Candy Total Utility Bars (utils) 0 0 1 27 2 3 4 5 6 (Click to select) 60 ♦ 76 Marginal Utility (utils) 27 19 Suppose Marco currently has two candy bars. You tell Marco you will give him either a soda, which gives him 28 utils of happiness, or two additional candy bars. b. Which is he likely to prefer? 6 1
