Suppose Demi's utility function over leisure (Le) and the consumption good x is: U (Le, x) = (Le)iri You can assume that the price of x is 1, and that she has up to 24 hours available each day, during which she can either work (L) or take leisure (Le). a) Formulate Demi's utility maximization problem to find her demand function for leisure, as it depends on non-labor income and her wage. b) Suppose that, aside from the money she earns by working, Demi's only other income is a daily $30" transfer from her parents. Draw a graph showing her budget constraint, and her optimal choice when the wage is $5/hour". In the space below, enter the number of hours of leisure she takes at this wage. (For non-integer values, you can round to within 1-decimal precision.) c) In a new graph, draw (approximately) Demi's labor supply curve, marking the points where the wage is $5, $10, and $20. Label your axes carefully