Given the following utility function: and marginal utilities: A consumer facing the following prices: chooses to consume Assume that graphically good X is on the horizontal axis and good Y is on the Given this consumption bundle, the marginal rate of substitution is equal to - Given this value, the consumer should consume U = 2X + 2Y MU, -2, MU, = 2 P, = $2, P, -5 15 units of good X and 19 units of good Y. vertical axis. (Round your answer to two decimal places. Note that the minus sign is already included.). in order to maximize his/her utility.

Given the following utility function: and marginal utilities: A consumer facing the following prices: chooses to consume Assume that graphically good X is on the horizontal axis and good Y is on the Given this consumption bundle, the marginal rate of substitution is equal to - Given this value, the consumer should consume U = 2X + 2Y MU, -2, MU, = 2 P, = $2, P, -5 15 units of good X and 19 units of good Y. vertical axis. (Round your answer to two decimal places. Note that the minus sign is already included.). in order to maximize his/her utility.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q.7 A consumer's utility function is given by the expression: U = (0.6A"' + 0.47'"s} Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.
Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 4[A-4 + B-4-4 + 40. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method b. Suppose PA increases. Show graphically the income, substitution effect and total effect and explain c. Suppose PA increases. Show the graphs for CV and EV and explain. One graph for CV and one graph for EV
b) As in question 2a, A consumer has a utility function given by U = x°.25 y0.75 and has an income of £100, the price of good x is £5 and the price of good y is £10. Suppose the price of good y falls from £10 to £5. By how much does the demand for good y fall and how much of the resulting change in demand for good y is due to the substitution effect and how much is due to the income effect? Take a picture of your diagrams and upload with your answer
Consider the following utility function: U= 100x0.50,0.50 A consumer faces prices of P, = $2 and P, =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y O étv MacBook Air 80 esc F1 F2 F3 F4 F5 F6 F7 F8 # $ % & 1 2 7 Q W E T Y tab S D F G caps lock C V M ft control option command つつエ B N
Consider the following utility function: U = 100x°.50,0.50 A consumer faces prices of P, = $2 and P, =$1 Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. 15 stv МacВook Air 80 DI esc F1 F2 F3 F4 F5 F6 F7 F8 @ %23 2$ & 1 2 4 6 7 8 Q W T Y tab A S F H J K aps lock C V M control option command B H
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A consumer's utility function is given by u (r_y) := r'/2y}/2 for any nonnegative x and y, representing the consumption quantities of goods x and y, respectively. Suppose that the price of good y is constantly ¢1, and that the consumer is given income m cedis (and nothing else). Denote p, for the price of good r. Based on the quantity demand (p, m) for good r. a. Given that p, > 1/(4m), calculate i (Pz, m) and (Pz, Py, m), then use the Slutsky equation to deduce what the substitution effect r° (pz, y) is equal to. b. Given that p, < 1/(4m), calculate i (P, m) and i (P2, Py, m), then use the Slutsky equation to deduce what the substitution effect r° (Pz; y) is equal to. c. What is your interpretation of the your result in a and b above?
8. Fabian consumes X and Y and the following utility function represents his utility: U = 2XY a. With a utility function of U = 2XY, Fabian's MU, = 2Y and his MU, = 2x ,where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). b. Suppose Fabian's income is $120 and Px = S6 and Py-$2, where Px is the price of X and Py is the price of Y. Write an equation for Fabian's budget constraint. c. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve: d. If Fabian is spending all of his income, how much X and how much Y will he choose? Use the equations you wrote in part's b and c to answer this question. e. What will Fabian's utility be with this combination of X and Y? f. Now suppose the price of X increases to P.=10. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve. How will this change the optimal combination of X and Y? What…
2. Lola consumes good x and y, and her marginal rate of substitution is 3/2, regardless of how many units of x and y that she consumes. Assume Lola has an income of $200 and that P-$5. (a.) Find Lola's optimal consumption bundle when px = 6. (b.) Find Lola's demand for x as a function of p,, assuming the price can be any non- negative amount.
Consider the following utility function: U= 4X + Y. A consumer faces prices of P, = $2 and P, =1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 10 units of good X and 19 units of good Y. Then the marginal rate of substitution (MRS) is equal to: MRS = (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) étv Help Me Solve This eText P MacBook Air 80 DII esc F2 F3 F6 F8 F1 F4 F5 F7 @ 23 2$ & 1 2 4 6 7 8. Q W E R T Y U tab A S G caps lock C V shift fn control option command ーのエ B レ

Consider the following utility function: U = 100x.50,0.50 A consumer faces prices of P, = $2 and Py =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X an units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y 15 tv MacBook Air 80 esc DII F1 F2 F3 F4 F5 F6 F7 F8 @ #3 % 2 7 8. Q W E Y tab s lock A S F G H J Z C V N M Onteel 8 : < CO T D