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 pays 10% of his wage income as tax. Show all the steps, with definition of every new notation used in the steps.

a) Suppose that Luke's pre-tax wage is $5/hour. Find Luke's daily budget constraint equation and graph it.

b) If Luke's pre-tax wage is $5/hour, what is Luke's optimal consumption, ( , )?

c) Assume that the pre-tax wage is an unknown variable, . What is Luke's leisure demand ()?

d) What is Luke's reservation wage, the lowest wage Luke is willing to work for?