This question shows how a simple two good model of consumption can be used to model a variety of choices, such as consumers' choices of how much to work, i.e. their labor supply. Suppose consumers derive wellbeing from leisure and consumption, represented by a differentiable, strictly increasing utility function u(l,q), where l0 denotes a consumer's amount of leisure and q0 their consumption. Suppose a unit of consumption costs p. In order to afford consumption, a consumer can provide an amount of labor L at wage rate w, with the constraint that there are only 24 hours in a day, which can be spent on labor or leisure: l+L=24 (a) Write down the consumer's utility maximization problem over labor and leisure. (b) Write down a necessary first-order conditions for an (interior) optimal solution in terms of the marginal rate of substitution between leisure and consumption, the wage rate, and the price of consumption. Interpret. (c) Draw a budget constraint, an optimal solution, and the indifference curve at the optimal solution. Your figure should also label the amount of leisure, consumption, and labor supplied by the consumer at the optimal solution. (d) Now imagine there is an increase in the cost of consumption p due to inflation. How does this affect the budget set? What predictions, if any, would you make regarding the consumer's optimal consumption and supply of labor