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.)

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.)

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section6.A: Indifference Curve Analysis

Problem 7SQ

See similar textbooks

Similar questions

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
5
Consider a consumer with the utility function u(x1,x2) = x11/3 x22/3. a. Find the Marginal Utility for each good. b. Find the slope of one of this consumer's indifference curves c. Write down the consumer's budget constraint. d. What is the slope of this consumer's budget constraint? Show how you derived 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 + 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)
Greg has the following utility function: u = x1^0.361x 2^0.642. He has an income of $74.00, and he faces these prices: (p1, p2) = (9.00, 8.00). Suppose that the price of x1 increases by $1.00. Calculate the equivalent variation for this price change.
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 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)
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)
Consider the following utility function: u(x1,x2) = x1 + x2. (A): i) Restate the consumer problem. ii) Form the Lagrangian function. iii) Find the first-order-conditions (FOC). iv) Divide Lx, by Lx,- v) From iv), can you determine the type of goods 1 and 2 are? (В): Draw the indifference curves for U = X1 + x2, where U = 1 and 2. What happens to the optimal demand for good 1, when: P1 P2 1. 3. Pi = P2
Suppose a consumer has utility function U(X, Y) = X2/3Y1/3. Suppose the consumer has M =$90 to spend and the prices of goods X and Y are PX = $15 and PY = $6 . a. Carefully express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the…
Please don't provide handwritten solution ...
Consider the following utility function for goods x1 and x2: u(x1,x2)=(x1+x2)2 What type of preferences does this utility function represent and why?
please give answer step by step