In our discussion of the permanent income hypothesis we categorized income as either permanent or temporary. Furthermore, we categorized people as either "consumption smoothers" or "hand-to- mouth." c. Using the notation below, with superscripts S and H for smoothers and hand-to-mouth consumers, write (a) mathematical statement or statements comparing these marginal propensities to consume. You may need to refer to your notes. MPC Perm, MPCFemp, MPCPerm, MPCHemp H d. Next, write a generic linear consumption function (using constants like 'a' for the intercepts) for both groups, i.e., CS (Yperm, YTemp), CH (Yperm, YTemp) e. Suppose aggregate consumption is the sum of consumption in each group. Let p ( < 1) equal the proportion of consumption smoothers in the population. The proportion of hand-to- mouth consumers is therefore 1-p. Write an equation for aggregate consumption, C(Yperm, YTemp) that combines your equations from part d, adjusted by the proportions. Explain your reasoning and define your terms as needed.