Help with Microeconomics Ques

Josh likes to eat Bananas (b), and Fish (f). His preferences are Cobb-Douglas, and can be presented by the utility function u(b, f ) = (1/5) (b − 2)(f + 3). Each banana costs 25 dollars and each fish costs 12 dollars. Josh has $314 to spend. Assume that bananas and fish are both perfectly divisible goods.

(a)  Find Josh's optimal bundle.
(b)  Suppose that Josh is now $75. What is his optimal bundle now?
(c)  Now, consider the general case, where Josh's income is m, the price of bananas is pb, and the price of fish is given by pf . In other words, treat fish as the numeraire. Find Josh's demand for each good in terms of m, pb and pf .
(d)  Find the good on which Josh will always spend more than half of his income.
(e)  Find the own-price, cross-price, and income elasticities of good 2 (fish).

Microeconomics
Matchmaticians Alumnus Matchmaticians Alumnus
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  • Savionf Savionf
    +2

    This is not my area of expertise, but the offered bounty is too low for a multiple-part question.

  • Alessandro Iraci Alessandro Iraci
    +1

    I don't know what part e) means, but I can answer the rest.

  • Kav10 Kav10
    +1

    Low bounty!

  • Mathe Mathe
    0

    I think you have a typo on the utility function. I could solve all the questions are you have presented them, except d.

    • Matchmaticians Alumnus Matchmaticians Alumnus
      0

      The utility function is u(b,f)= 1/5(b-2)(f+3). Or is it something else?

    • Mathe Mathe
      0

      Nevermind, the utility is ok!

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Mathe Mathe
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