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Suppose you are given the utility function U(C, l) = lnC + 2L, where C = consumption and 0.4 0.6 L = leisure, and the

  1. Suppose you are given the utility function U(C, l) = lnC + 2L, where C = consumption and
  2. 0.4 0.6 L = leisure, and the production function Y = zK N .
  3. Assume that all output is consumed (Y = C), and that hours of leisure/work are normalized as representing fractions of a day (or equivalently, a value of 1 represents 24 hours).
  4. Suppose z = 1 and K = 20.
  5. a) What are the Pareto-optimal hours of work? b) What are the Pareto-optimal hours of leisure?
  6. Given the efficiency wage function: e(w) = w - 18w + 96w . What is the optimal wage
  7. that the firm should set?

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