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After spending a significant time meditating, your friend René has discovered a deep truth about his...

After spending a significant time meditating, your friend René has discovered a deep truth about his preferences, that is, what makes him happy. René’s has realized his preferences over two goods, ?1 & ?2, can be described by the following utility function ? (?1, ?2 ) = 3?1 3 4?2 1 4 . a. Using whatever constrained maximization technique you prefer, find René’s optimal bundle of goods, (?1 ∗ , ?2 ∗ ), given his budget constraint: ? = ?1?1 + ?2?2. Be sure to show your work for full credit! b. Using your results from part (a), find René’s optimal bundle if he has $80 and the prices are P1=$1 & P2=$2. c. Draw a rough graph René’s indifference curve and budget constraint from part (b). Clearly label his optimal bundle of goods. d. Given your answer to (a), how does Rene’s consumption of good 1 depend on the price of good 2? e. Is your answer to part (b) a corner solution? If so, explain why. If not, draw a graphical example of a corner solution with preferences and a budget constraint.

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