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, ½) and (5, 10)

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, ½) and (5, 10)

Economics For Today

10th Edition

ISBN:9781337613040

Author:Tucker

Publisher:Tucker

Chapter6: Consumer Choice Theory

Section6.A: Indifference Curve Analysis

Problem 11SQ

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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)
A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her optimal X consumption? (like, x >/ 7 or 10 >/ x >/7…etc. Use indifference curve analysis on a graph to reason about the possible locations of the new optimal bundle.)
Could Figure 3.2 be a single indifference curve if preferences are monotonic?
2 Indifference curves Suppose an individual who derives utility u(x, y) from consuming a units of good X and y units of good Y. Derive the indifference curve for a level of utility U for each of the following utility functions. Draw them in the graph below for a utility level U = 18. (A) u(x, y) = 2x + 3y (B) u(x, y) = min{3x, y} (C) u(x, y) = xy
Suppose an individual has a utility function u (x1, x2) = 2*2. Present your mathmatical expressions below in the simplest form you can. a) Derive an expression for the marginal utility of good 1, and for the marginal utility of good 2. b) Using these, solve for an expression describing the slope of an indifference curve: MRS (11, 12). c) Sketch indifference curves for this consumer corresponding to u = 0,10,20. (Hint: z rı = k solves for m} = 11 (21) . Solve this expression and approximate it on a graph for the three values of k.)
John has a utility function for goods x1 and x2 which is represented by u(x1,x2)=x10.2x20.8. Assume her income is 100 TL and the prices of x1 and x2 are 10 TL and 20 TL, respectively. a) Express the marginal rate of substitution (MRS) between goods x1 and x2. As the amount of x1 increases relative to the amount of x2 along the same indifference curve, does the MRS increase or decrease? Explain. b) Derive the demand functions for goods x1 and x2.
A utility maximizing consumer with preferences u(x, y) - x2y1/2 allocates 60 dollars towards the purchase of goods x and y. Prices are py - 0.5 and px – 1. With the purchase of a discount card prices are py - 0.5 and px - 0.25. Calculate the maximum fee the consumer should pay to purchase this card. Provide an Indifference Curve and Budget Line Diagram to illustrate and quantify the Substitution Effect (a to b) and Income Effect (b to c) of this price change. Quantify all intercepts and intersections.
1. Joan is on summer break and spends most of her time either playing video games or browsing the internet. Her utility function is U (q1, 42) 399.24$, where qi represents the 0.2,0.8 %3D hours spent browsing the internet and q2 hours playing video games. Joan does not have a budget constraint but she has 15 hours to spend on both activities. (a) Write the equation for one of Joan's indifference curves when the level of utility is equal to 100. (b) Write Joan's time constraint. (c) Find the amount of hours that Joan will spend on each activity that maximizes her utility and satisfies her time constraint. Use either the substitution or Lagrangian method. (d) Can Joan afford any bundle that yields a utility of 50? Explain. (e) How does Joan's optimum amount of time spent on each activity change if her utility function is U (q1, q2) = 5ln(3) + In(q1) + 4ln(q2)?
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)
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…
Every week Chris consumes 14 medium-sized pepperoni pizzas, which cost $10.00 each, and 22 galions of ice cream, which cost $15.00 each. Chris' marginal utility of pizza at that point is 2.75 and marginal utility of gallons of ice cream is 3.30. Comment on Chris choice (economically speaking, not nutritionally) and illustrate with an indifference map (Pizza on the y-axis, ice cream on the x-axis).
Suppose Tom has $60 in income and only buys cheese and tuna. Walmart charges $2 for a can of tuna and $4 for a block of cheese. Tom shops at Walmart and buys 20 cans of tuna and 5 blocks of cheese. a) Draw the budget constraint and indifference for Tom (put Tuna on X-axis). b) Suppose Tom’s income increases to $100, and his consumption of cheese increases to 6 blocks. Draw the new budget constraint and new optimal consumption bundle. c) Is tuna a normal or inferior good for Tom? Draw the Engel curve of tuna.