QuestionQuestion 3 $\mathrm{Le}_{3}$ [25 marks] Anna's utility function over wine and garbage disposal is $\mathrm{UA}_{\mathrm{A}}=\mathrm{W}_{0.5} \mathrm{G} 0.5$ , and Brewster's utility function is $\mathrm{U}_{\mathrm{B}}=\mathrm{W}_{0.67} \mathrm{G} 0.33$ . Anna has 2 bottles of wine and 5 units of garbage disposal services. Brewster has 3 bottles of wine and 3 units of garbage disposal services. (a) In an economy with no exchange, what are the utility levels of Anna and Brewster?

Studdy Solution
Simplify and calculate Brewster's utility level.
$\mathrm{U}_{\mathrm{B}} = 3^{0.67 + 0.33}$
$\mathrm{U}_{\mathrm{B}} = 3^1$
$\mathrm{U}_{\mathrm{B}} = 3$
Solution: The utility levels in an economy with no exchange are:
- Anna's utility level: $\sqrt{10}$ - Brewster's utility level: $3$

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