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Jane is choosing where to live:   In city A she will earn $3000, but the price...

Jane is choosing where to live:  

  • In city A she will earn $3000, but the price of food is $10 while the price of luxury goods is $20.  
  • In city B she will earn $2100, the price of food is $14, and the price of luxury goods is $5.  

Jane’s utility function is given by ?(?1, ?2) = ?16?23 where ?1 is units of food and ?2 units of luxury goods.

  1. Calculate the quantity demanded of food and luxury goods if she were to live in city A. Be sure to write the consumer problem, the associated Lagrangian and the first order conditions.
  2. Calculate the quantity demanded of food and luxury goods if she were to live in city B. Be sure to write the consumer problem, the associated Lagrangian and the first order conditions.
  3. Now using what you found in question a) and b), where is she going to live? Why?
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