Q.7 A consumer's utility function is given by the expression: U = {0.6x"s + 0.4y"s). Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? - .5
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- Is it possible for total utility to increase while marginal utility diminishes? Explain.A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1. Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.Please no written by hand and no emage Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils.a) Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b) Calculate the optimal weekly consumption bundle for this consumer.c) Does the consumer view C and S as complements or substitutes?
- Mylie’s total utility from singing the same song over and over is 50 utils after one repetition, 90 utils after two repetitions, 120 utils after three repetitions, 80 utils after four repetitions, 20 utils after five repetitions, and -60 utils after six repetitions, as shown in the table below. a. Write down her marginal utility for each repetition. Instructions: Enter your answers as a whole number. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Repetitions Total Utility Marginal Utility 0 0 — 1 50 2 90 3 120 4 80 5 20 6 -60I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?Mylie's total utility from singing the same song over and over is 70 utils after one repetition, 110 utils after two repetitions, 140 utils after three repetitions, 160 utils after four repetitions, 120 utils after five repetitions, and 60 utils after six repetitions, as shown in the table below. a. Write down her marginal utility for each repetition. Instructions: Enter your answers as a whole number. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Repetitions 0 1 2 3 4 5 6 Total Utility Marginal Utility 0 70 110 140 160 120 60 b. Once Mylie's total utility begins to decrease, does each additional singing of the song hurt more than the previous song or less than the previous song? O More than the previous song O Less than the previous song
- A consumer is making purchases of products Alpha and Beta such that the marginal utility of product Alpha is 63 and the marginal utility of product Beta is 40. The price of product Alpha is $9, and the price of product Beta is $5. The utility-maximizing rule suggests that, to stay within a given budget constraint, this consumer should Multiple Choice O O O increase consumption of product Beta and increase consumption of product Alpha. make no change in the consumption of Alpha or Beta. increase consumption of product Beta and decrease consumption of product Alpha. increase consumption of product Alpha and decrease consumption of product Beta.solutions. Question 1 Calculating MRS for CD Utility Functions (a) If a consumer has a CD utility function 0.4 0.6 U(91,92) = 994926, calculate MRS1,2. (b) If a consumer has a CD utility function Ima kdown1 calculate MRS1,2. (c) If a consumer has an utility function noltan asd Tor sympy ,1-α U(91,92) = 91 92 llib et (.) orde (hing aid tol bholup U(91,92) = a ln(91) + (1 - a) ln(92), diw sonuanos of calculate MRS1,2. Is it the same as the result in the previous part? (Note: Recall that we discussed the concept of ordinal utility in class, which means only the order of utility matters, not its magnitude. In function is a monotone transformation on the CD utility function. Notice that In (qq) = a ln(9₁) + (1 - a) ln(92). This example verifies that a monotone transformation does not change *(S) sidshav the consumer's indifference curves.) wobei/ (d)A consumer has the following utility function: Ulx, y) = xy -y, *21 where x and y represents the quantities consumed of goods X and Y. y 20 What will be the substitution and income effects for X and Yassuming that the consumer attempts to maintain the same level of utility achieved before price of Y increased (that is, when price of Y was $1)? SEx= +0.5 IEx = -0.5 SE, = -0.25 IE- = -0.25 SEx= +0.293 IE = -0.293 SEy = -0.414 IE, = +0.414 SEr= +0.25 IE SE, = -0.75 IE, = -0.75 = -0.25 SEx= +0.414 IEx = -0.414 SEy = -0.293 IE, = -0.207 Income = $3 Px= $1, Py= $2
- 39. The following chart shows thec total utility-that Ammar receives from çonşuming various amounts-of chocolate.candy bars each day: Number candy, bars consumed për đay Total'utility 1' 40- 2 70 90 100 4. 80 Which of the following statements about Ammar's marginal utility is correct? Hiş marginal utility from the first candy bar is greater-than his marginalutility from the second candy' barWhich among the following is not true?Select one:a. None of the answers are correctb. When marginal utility declines, a higher price is needed to induce the consumer tobuy more of a particular productc. When marginal utility declines, a lower price is needed to induce the consumer tobuy more of a particular productd. All the answers are correcte. Utility maximizing rule and the demand curve are logically consistentI need help with my homework assignment that i dont undertsand. Suppose a consumer has a utility function given by U(X,Y) = MIN(X, 2Y). The consumer has $90 to spend (M = $90). The Price of good Y is PY = $1. Using a graph, sketch the consumer’s demand curve for Good X. Make sure to identify three points on the demand curve. Make sure your graph is neat, accurate, and scaled properly.