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Each day, Luke must decide his leisure hours, L, and his consumption, C. His utility function...

Each day, Luke must decide his leisure hours, L, and his consumption, C. His utility function is given by the following equation

?(?, ?) = (? − 30)(? − 12).

Luke receives $50 welfare payment per day. Show all the steps, with the definition of every new notation used in the steps.

  1. a) Suppose that Luke’s hourly wage is $5. Find Luke’s daily budget constraint equation and graph it. (5 pts.)

  2. b) If Luke’s wage is $5 per hour worked, what is Luke’s optimal consumption, (? , ? )? (5 pts.)

  3. c) Assume that the wage is an unknown variable, ?. What is Luke’s leisure demand ?(?)? (5 pts.)

  4. d) What is Luke’s reservation wage, the lowest wage Luke is willing to work for? (3 pts.)

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