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.

Sample Solution

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