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I need help with understanding this question. Shelly's preference for consumption and leisure are given by U(C,L) = (C-100)(L-40). There are 110 hours in a

I need help with understanding this question.

Shelly's preference for consumption and leisure are given by U(C,L) = (C-100)(L-40). There are 110 hours in a week available to split between labor and leisure. Shelly earns $10 per hour. She also received $320 worth of assistance benefits each week regardless of how

much she works.

  1. Graph Shelly's budget constraint.
  2. What is Shelly's marginal rate of substitution when L = 100 and she is on her own budget line?
  3. What is Shelly's reservation wage?
  4. Find Shelly's optimal amount of consumption and leisure.
  5. The government now imposes tax on labor earnings= 0.2. How many hours will Shelly work in this case? Hint: The proportional tax on earnings means that, if the wage is w, then the after-tax wage is (1-)w. Solve Shelly's problem again with her after-tax wage.

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