3. Food and Gasoline (20 pts) Suppose we have a model of a consumer choosing between labor and consumption. Instead of a single consumption good instead they choose both food and gasoline, represented by Fand G, respectively Their per-period utility function over Food, Gasoline, and leisure, [, is given by U(F,G,1) = In(F + G) +Inl We will suppose that Food and Gasoline have the same cost of 1 (i.e. don't worry about prices), individuals have exactly 24 units of time which they divide between labor and leisure so that | =24 N. Individuals receive a wage of w for each unit of time that they work and no income from any other sources. (a) (5 pts) Write out the budget constraint of the household (b) (5 pts) Set up the Langrangian for the household take First Order Conditions. (Do not Combine just label each FOC) (c) (5 pts) Now let us redefine things a little bit, let us call aggregate consumption C. Define aggregate consumption C=F+G Now making this substitution into your First Order conditions (note some of your FOCs may become redundant), combine your first order conditions to create the intratemporal optimality condition (d) (5 pts) Solve for labor supply. What can you say about the relative impact of the substitution and wealth effects with respect to an increase in the wage