Suppose that we have a consumption function of the form

C = 220 + 0.9×Yp,

where Yp is permanent disposable income. Suppose that consumers estimate their permanent disposable income by a simple average of disposable income in the present and previous years:
Yp== 0.5×(Yd + Yd-1),

where Yd is actual disposable income.

a. Suppose that disposable income Yd is equal to $4,000 in year 1 and is also equal to $4,000 in year 2. What is consumption in year 2?

b. Suppose that disposable income increases to $5,000 in year 3 and then remains at $5,000 in all future years. What is consumption in years 3 and 4 and all remaining years? describe why consumption responds the way it does to an increase in income.

c. What is the short-run marginal propensity to consume? What is the long -run marginal propensity to consume?

d. describe why this formulation of consumption may provide a more accurate description of consumption than the simple consumption function that depends only on current income.