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- o Suppose a u (X,, X)= x" x,** and facer 9 {,x, + P, Xa = M. joud 1 and utility funtion baiget coust ain t functinn for Consumer has a 180 Derive ber damend good Venify that beath functon 2. owe himo qenousfonsumer's demand xy for two different and the consumer's in come is $72. different Consumer's demand xy for chosen to maximize two the శ్రిందికి goods are x² lefility function The per respectively unit of , and the Consumer's in come is $7 x and y are $3and $4. 22,2 © telrite out the fagrangean for the Constrained maximization problem © Find the utility maximizing demands for both goods and he Larange multiplier, 2 o What is the change in consumer's ufility if income Changes from $72 to $75Mylie’s total utility from singing the same song over andover is 50 utils after one repetition, 90 utils after tworepetitions, 70 utils after three repetitions, 20 utils afterfour repetitions, 250 utils after five repetitions, and 2200utils after six repetitions. Write down her marginal utilityfor each repetition. Once Mylie’s total utility beginsto decrease, does each additional singing of the songhurt more than the previous one or less than the previousone?
- Suppose an indinidual has the following utility finction Urey)-2+2" writh a strictly ineveaseng morrginal rate of substitntion. and income of 3 The price of y is $4 CPpi ) The intial price of x is $lcre=) and then increases to 3 px=3). Find the chonge in the quantidy consumed of X.IHow much of the chonge is the income effect? How much by the Substitution effect? Evplan in Econ terms erplainedl bya. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?ceriuppose that Isaiah has a weekly fixed budget and spends it all on haircuts and ice cream. At his current combination arof consumption, the marginal utility of the last dollar spent on haircuts is greater than the marginal utility of the last dollar spent on ice cream. Has Isaiah maximized his utility? A C E Yes, because changing his current consumption combination will reduce his total utility B No, because he can increase his total utility by purchasing more haircuts and D fewer ice creams Yes, because he has purchased 2 goods in proportion so that he can get- the maximum utility from each Yes, because he purchased the maximum possible with a limited budget No, because he can increase his total utility by purchasing fewer haircuts and more ice creams
- What price ÅSsuming do you line and budget that understand by line? Consumer has income of $180, which monthly he Spends Good' X on two commodities and Grood Y. The price l07 Good $13 and price of the is $24. What would ' be Combinations of Crood X is Various Good Y this combinations line regard? and in and write draw various budget according ly?Mike has a decreasing marginal uity of income We know that Mike's income in greater than S10, but we de not know his exact inome Adam offers Mika the folloeing bet Adam wil throw a fair coin (that is, heads and tals have equal probatilty) a heada. Mke pays Adam $10. ta Adam pays Mke S10 What can we conclude from this infonmation? O Mike will reject the bet only it his income is high emought Ob. Mike will reject the bet, independently of how high his income is Oc Mke wil accept the bet independently of how high his income is Od Mke will accept the bet only if his income is high enought O Mka will always be indiferent between accepting and rejecting the bet39. 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' bar
- Five consumers have the following marginal utility ofapples and pears:Marginal Utilityof ApplesMarginal Utilityof PearsClaire 6 12Phil 6 6Haley 6 3Alex 3 6Luke 3 12The price of an apple is $1, and the price of a pear is$2. Which, if any, of these consumers are optimizingtheir choices of fruit? For those who are not, howshould they change their spending?Price per arginal Utility Fron Current Consumption Product Unit $ 10 20 20 30 The table shows the marginal utite derived trom curent consumpton leves of three new products. A B and C at are being sold in the maet at the prces isted The contumer can imniediately gan the most extra total utity by winching spending from Mnple Choce ANEJeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can either call her on the land-line phone for five cents per minute or he can drive to see her, at a round—trip cost of 2 in gasoline money. He has a total of 10 per week to spend on staying in touch. To make his preferred choice, Jeremy uses a handy utilimometer that measures his total utility from personal visits and from phone minutes. Using the values in Table 6.6, figure out the points 011 Jeremys consumption choice budget constraint (it may be helpful to do a sketch) and identify his utility-maximizing point.
