Consider a labor supply model. The decision maker has utility over leisure L and consumption goods c given by u = 2L + c. They have 10 available hours and no non-labor income. The wage rate is w = 20 and the price per unit of consumption is p = 1.

a) Use the tangency method to find the consumer's optimal choice of L and c. Based on your calculations, if this person had more available hours, would they have worked more, less, or the same number of hours?

b) Say that the situation is the same as before except that after 7 hours of work the wage rate increases from w = 20 to w = 30. Sketch the budget set for this situation on the usual axes, with axes, intercepts, and slopes all labeled.