Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y − 3.5)^2
Further assume that the price of good x, px = $6, the price of good y, py = $8 and the individual has an income m = $65
a) (5 points) Draw an indifference curve (one IC is enough) that represents this person’s preferences. Please label the graph properly including values for x and y.
b) (5 points) Intuitively, and without formally solving, can you guess the maximized values x* and y* for the above utility function. Explain your answer.
c) (7.5 points) Derive the optimal values x* and y* by formally solving the above utility function subject to the above constraint. You can use any of the utility maximization techniques we learned in class.
d) (7.5 points) Compare your answers in parts b) and c). Based on the utility function that is given in this problem as well as the budget constraint, can you explain the differences between the answers you found in parts b) and c) (if any). Be as detailed as possible with your explanation.
Presentation Portrayal is a significant piece of any narrating, and it is consistently present in films. A specific film named The Five-Year Engagement is coordinated by Nicholas Stoller and is delivered by Judd Apatow, Rodney Rothman, and Nicholas Stoller. It is a satire with some sentiment which fixates on a couple who experience issues sorting out their life so as to get hitched. The challenges originate from all headings, including individual issues and family members (Apatow, 2012). Examination From the earliest starting point, the indications of portrayal are self-evident. Account structure is composed and connected in a chain of functions and in the initial scenes, Tom Solomon begins recounting an account of how himself and his life partner, Violet Barnes, have met a year back. An existence impact is made through the flashback, and it is conceivable to perceive how the two characters were unique but, especially the equivalent. The circumstances and logical results are an enormous piece of any portrayal thus, it is clear how being at a gathering and witnessing over at one another is the reason for the relationship to start. The request for functions is plainly delineated from the beginning, and the watcher fills in all the functions that occurred inside the time of the couple dating. The flashback in time is a detachment from the primary story, as it upsets the sequential request of functions. It merits referencing that occasionally, a few insights regarding the story are covered up, just to be appeared or uncovered later. This isn't the situation here, as the watcher is given the principal meeting of the couple. It must be noticed that the flashback and the functions portrayed have to some degree a blended length (Bordwell and Thompson, 2010). Despite the fact that it a snappy memory of past functions, a few pieces of the account, explicitly the main words the characters trade, are eased back down, so the watcher can feel the impact of the couple's delay as expected. Another significant portion of the portrayal is the recurrence or redundancy of specific functions or scenes. A comedic impact is made with the high number of redundancies in the photos of Tom's past sweethearts. The past is being described in an extraordinary number of pictures from an earlier time, and once more, the watcher tops off the character's past with various functions. Space is likewise remembered for the portrayal, as makes a particular air with its association with the scene (Bordwell and Thompson, 2010). The commitment party for Tom and Violet is set in a lawn, and despite the fact that there is a great deal of room, the seats and visitors are situated intently together. This tells the crowd that the family is close, however an intriguing turn happens when individuals begin talking. It is made evident that despite the fact that individuals are situated intently there are portions of their carries on with that are obscure and new to one another. This separations the characters, despite the fact that the actual area is close. The entire start of the film is an initial scene; as the watcher doesn't yet have the foggiest idea where the story will go and what inconveniences the characters will insight. The advancement of the plot happens in a positive portrayal with the couple preparing to be hitched. In a more extensive and more broad sense, portrayal comprises of functions that make a stream yet are independent from one another in the story. Despite the fact that they are each of the a piece of the plot, the division gives the crowd a feeling of time entry. At the point when Tom and Violet choose to defer the wedding and move to Michigan, it tends to be viewed as the main significant chain of functions. The wedding of Violet's sister and the demise of the grandma was nearly minor in the story on the grounds that the couple would at present remain in their town. The move is the significant change in the account, and an entire distinctive setting rises. Despite the fact that the portrayal happens in an alternate area there is some reiteration of the functions. At the point when the teacher meets Tom and violet, he solicits them to recount a story from how they met. The watcher is then given a reiteration of a flashback as expected. Yet, the storyteller is changed; while already it was Tom recounting the account of their gathering, here, Violet additionally remembers herself for the portrayal which adds a feeling of fellowship. With the further movement of the film, functions change quickly and portrayal is a lot of unique in relation to the start of the story. Toward the beginning of the film, it was glad and streamed effectively, yet towards the end, the portrayal turns out to be more rough and apprehensive, as the couple is appeared to float separated. The consummation re-visitations of the beginning of the film where Tom and Violet are glad and this makes the story ceaseless. The peak of the story is additionally towards the end, as the crowd contemplates whether the couple will remain together, and this adds tension to the portrayal. End Taking everything into account, the film had numerous types of portrayal, and the trade of styles added a remarkable contort to the functions. The film is prescribed to all who appreciate satire with sentiment.>GET ANSWER