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    Consider a consumer who can do the following things:
    • spend his money m on casual gaming on cellphone,
    • work in his backyard, growing artisan tomatoes Q and selling
    them for price p, or
    • buy and consume tomatoes T for the price p.

    The utility function of such a consumer is U(m, T, Q) = m + p(Q −T) + V (T) − W(Q), where both V and W are increasing, V (T) =2 ln T, W(Q) = Q2

    a) Derive this consumer’s function of demand for tomatoes.

    b) Derive this consumer’s tomato supply function. Solve for the price
    of tomatoes in autarky.

    c) Assume there is also this consumer’s brother, who has an identical
    utility function. Would the market-clearing price change? Explain.

    d) Assume the brother dislikes working, and his utility function is
    instead
    U(m, T, Q) = m + p(Q − T) + V (T) − 4W(Q).
    What would be the brother’s choice if the brother was living in solitude,
    independently, in autarky?

    e) What is the total demand of two brothers as a function of the
    tomato price? What is the total supply of two brothers as a function
    of price? Show that the trade between brothers improves the
    welfare.

    f) Explain why trade between brothers made them better off, when
    one brother got lazier.
    .
 
 
 
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