I was just wondering what the steps one would take to maximize the utility of a function of the form U(X,Y) = min{X,Y} + X subject to income I = p x X + p y Y where p x is the price of X and p y is the price of Y. I understand that normally this would be solved using the Lagrangian method but obviously you cannot differentiate this particular function.

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I was just wondering what the steps one would take to maximize the utility of a function of the form U(X,Y) = min{X,Y} + X subject to income I =       p    x  X +       p    y  Y where       p    x   is the price of X and       p    y   is the price of Y. I understand that normally this would be solved using the Lagrangian method but obviously you cannot differentiate this particular function.

1s1zubv · Accepted Answer

I would make a case decisions. Find out, what happen in all these cases.1)   max        U  (  X  ,  Y  )  =  Y  +  Xs.t.   Y  ≤  X and   I  =      p    x    X  +      p    y    Ya)       p    x    ≤      p    y  b)       p    x    &amp;gt;      p    y  2)   max        U  (  X  ,  Y  )  =  2  Xs.t.   Y  ≥  X and   I  =      p    x    X  +      p    y    Ya)       p    x    ≤      p    y  b)       p    x    &amp;gt;      p    y

I was just wondering what the steps one would take to maximize the utility of a function of the form

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