Economics : Simplify the consumption function

Economics : Simplify the consumption function

Subject: Economics    / Accounting
Question

Suppose the consumption function is C = 4,000 + 0.6YD , where T = -1,100 + 0.25Y, and all units are in billions of $ per year.

A. Simplify the consumption function. Attach your work. When income rises by $1,000 billion per year, does C rise by mpc * $1,000 billion per year? Why or why not?

B. Suppose that the economy can be split into three groups. Group A are borrowers who fund their consumption of durable goods with borrowed money and are sensitive to changes in interest rates. Group B are retirees who fund their consumption from the earnings on their accumulated savings and are also sensitive to changes in interest rates. Group C consists of everyone else who are neither borrowers nor retirees, and for whom the interest rate is irrelevant to their consumption spending. Express the share of the population in group A as A / (A+B + C) and the share of the population in group B as B / (A + B + C). What is an equation for the consumption function that builds on the consumption function in the prompt but incorporates the behavior of groups A, B, and C? Defend your answer.