I’m working on a macro economics multi-part question and need an explanation and answer to help me learn.

In The General Theory of Employment, Interest, and Money, Keynes proposed “the

fundamental psychological law, upon which we are entitled to depend with great confidence both a

priori from our knowledge of human nature and from the detailed facts of experience, is that men are

disposed, as a rule and on the average, to increase their consumption as their income increases but not

by as much as the increase in the income.”

a. Using the notation from class, translate Keynes’ psychological law into a

mathematical statement

.b. Some people do not like fancy words or equations. Would you kindly sketch agraph, instead? Consumption should be on the vertical axis.

In our discussion of the permanent income hypothesis we categorized income as eitherpermanent or temporary. Furthermore, we categorized people as either “consumptionsmoothers” or “hand-to-mouth.”c. Using the notation below, with superscripts S and H for smoothers and hand-tomouth consumers, write (a) mathematical statement or statements comparing thesemarginal propensities to consume. You may need to refer to your notes.

d) Next, write generic linear consumption function (using constants like ‘a’ for theintercepts) for each of the two groups,

e) oppose aggregate consumption is the sum of consumption in each group. Let p (<1) equal the proportion of consumption smoothers in the population. The proportionof hand-to-mouth consumers is therefore 1-p. Write an equation for aggregateconsumption,?????????????????????????, ?????????????????????that combines your equations from part d, adjusted by the proportions. Explain yourreasoning and define your terms as needed.