1. (Maple worksheet)

2. There are three main cases: X=40, X<40, and X>40.

  1. X=40. In this case , we can say that Y>X for sure. With the new budget line, the worker will definitely not choose any point to the right of X, as those points were already available -and not chosen- before. Moreover, since at X, MRS=9, we know that MRS(X)<12, so that the worker will choose more hours of work. If the wage becomes $12 for all hours, and Y>X, the change represents a pure income effect, so that Z<Y. However, we cannot tell whether X>Z or X<Z. (see graph)

    2.  
  2. X<40. In this case, the introduction of overtime pay has both an income and a substitution effect. We know that the worker will not choose Y such that X<Y<40 (as such a choice was already available before). Similarly, she would not choose Y<X. However, it is possible that overtime pay makes the worker choose Y>40>X. Therefore, we have just two options, either X=Y or Y>40>X. As for Z, if X=Y, then we cannot tell. If Y>40, though, we know that Z<Y as in case i). (see graph)

    3.  
  3. X>40. In this case, the overtime pay has both income and substitution effects, so that we cannot tell whether X<Y or X>Y, but we still know that Y>40. As before Z<Y.