3.4 Constrained Application: Recorded tracks and live music 0.4 0.6 U = ● - Utility function: Budget constraint: Optimal choice: Consumer Choice 0 Y=30=0.59₁ +92 = P₁9₁ +P₂92 9₁ = 24,9₂ = 18
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explain how they find the quantities using MRS = MRT
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- Assume a consumer has a well-behaved utility function (e.g. strictly increasing, diminishing MRS) with an income of $80. Suppose the price of good X is $2 and the price of good Y is $8. Assuming the consumer has chosen the optimal market basket, what is the consumers marginal rate of substitution at that consumption level? Group of answer choices 4 not enough information 40 10 .25todd is a cattle rancher in june and july he spent his clothing budget on jeans and cowboy hats. each pair of jeans cost $56 and each hat cost $41. At Todd's optimal choice, his marginal utility from the last pair of jeans purchased is 592. This means that his marginal utility from the last cowboy hat purchased is: Round the final answer to the whole numberDerive the relationship between the quantity of X demanded and the price of X if the consumer’s indifference map vis-à-vis X and Y has curves concave to the origin. Let X be games of golf per annum and Y all other goods. Draw the indifference map and budget constraint of: (a) an amateur who pays to play golf; (b) a professional who is paid to play golf. May we conclude that golfers turn professional because they dislike the game?
- Suppose that a typical consumer’s utility function is characterized by the following relation between good X and good Y. The consumer’s consumption decision is influence by the price of the respective goods, which requires him 2 birr for each unit of X and 3 birr for each unit of Y and the resource available to him is 160 birr. A construct the budget constraint of this typical consumer Find the optimal consumption of X and YYou have £20 per week to spend, and two possible uses for this money: telephoning friends back home, and drinking coffee. Each hour of phoning costs £2, and each cup of coffee costs £1. Your utility function is U(X,Y) = XY, where X is the hours of phoning you do, and Y the number of cups of coffee you drink. What are your optimal choices? What is the resulting utility level? You can use the standard result on the constrained maximization of such a function, but must state it clearly. Now suppose the price of telephone calls drops to £1 per hour. What are your optimal choices? What is the resulting utility level? How much income per week will enable you to achieve the same quantities at the new prices as the ones you chose before? What income will enable you to attain the same utility as you did before? Comment on your answer in the context of equivalent variation and compensating variation.Q.3. Suppose a student has monthly income of Rs 10,000. He consumes only two commodities Sandwich and Shawarma. The cost of Sandwich is Rs 50 each, and the cost of Shawarma is Rs 100 each.a) Draw the student’s budget constraint. What is the slope of his budget constraint? b) Suppose student gets a raise, so his income increases from Rs 10,000 to Rs 12,000. Show what happens to consumer optimal consumption choice if both Sandwich and Shawarmaare normal goods. Now show what happens if Sandwich is an inferior good.c) Suppose consumer income decreases to Rs. 8,000. Show what happens if both Shawarmaand Sandwich are normal goods. Now show what happens if Sandwich is an inferior good.
- If Utility =.5lnX+3Z+10+4√W then Marginal utility from X is....;. and the Mu of Z is ..A consumer consumes two goods and her utility is form by Cobb-Douglas utility function. Her MRS is 0.9 * (q2/q1) Using these information find Marginal utility levels of first amd second goodsPlease show your answer step by step with reasons. (i) A consumer has income of £3,000. Apple juice is priced at £3 a bottle and cheese is priced at £6 a kilo. Draw the budget constraint for a consumer with standard preferences. What is the slope of this budget constraint?(ii) Show a consumer’s budget constraint and indifference curves for apple juice and cheese. Show the optimal consumption choice. If the price of juice is £3 a bottle and the price of cheese is £6 a kilo, what is the marginal rate of substitution at this optimum? (iii) The price of cheese rises from £6 to £10 a kilo, while the price of juice remains at £3 a bottle. For a consumer with a constant income of £3,000, show what happens to consumption of juice and cheese. Decompose the change into income and substitution effects.
- A consumer currently spends a given budget on two goods, X and Y, in such quantities that the marginal utility of X is 15 and the marginal utility of Y is 8. The unit price of X is $3 and the unit price of Y is $2. The utility-maximizing rule suggests that this consumer should Multiple Choice a. decrease consumption of product X and increase consumption of product Y. b. increase consumption of product X and increase consumption of product Y. c. decrease consumption of product Y and increase consumption of product X. d. stick with the current consumption mix because it yields maximum utility.If the marginal utility of the burger is greater than the price of the burger, we expect a rational consumer_______. Group of answer choices to spend more money on pizza. to purchase more burgers. to spend more money on beverages. to purchase less burgers.suppose the utility function of Vivian is U=602/3Y1/3. The unit priice of Good X is $10 while the unit price of Good Y is $30. Vivian has a budget of $1,800 to be spent on Good X and Good Y. Find the optimal consumption bundle of vivian show your calculations.
