Ivan faces a labor supply decision. His well-behaved preferences over the two goods \'hours of leisure\' L and \'consumption\' c can be represented by u= 4√L+c. He has no non-labor income and can choose how many hours to work at the wage rate w per hour. The price per unit of consumption is p, and his available free time is T hours.

a) Sketch Ivan\'s budget set, with axes, intercepts, and slope labeled (this will depend on the parameters w, p, and T).

b)  Use the tangency method to find Ivan\'s demand functions for leisure and consumption (as functions of w, p, and T).

c) Let\'s think about Ivan\'s "time expansion path" (that is, the analog of the income expansion path a.k.a. income-consumption loci but for changes in T). Sketch it and explain why it has this shape, with reference to Ivan\'s demand functions.

d) In terms of parameters from the model, what are the most that Ivan would be willing to pay to have an extra hour of free time (that is, to increase T by 1)? Why?