Question

2. Economists observed the only 5 residents of a very small economy and estimated each one’s consumer spending at various levels of current disposable income. The accompanying table shows each resident’s consumer spending at three income levels.

individual Consumer	Individual Current Disposable Income
	$0	$20,000	$40,000
Andre	1,000	15,000	29,000
Bob	2,500	12,500	22,500
Casey	2,000	20,000	38,000
Dianne	5,000	17,000	29,000
Elena	4,000	19,000	34,000

a) What is each resident’s consumption function? What is the MPC for each resident?

b) What is the economy’s aggregate consumption function? What is the MPC for the economy?

Answer 1

2)a)

Individual consumer	Autonomous Income	MPC	Consumption function
Andre	1000	(29000-15000)/(40000-20000)=0.7	1000+0.7Yd
Bob	2500	(22500-12500)/(40000-20000)=0.5	2500+0.5Yd
Casey	2000	(38000-20000)/20000=0.9	2000+ 0.9Yd
Dianne	5000	(29000-17000)/20000=0.6	5000+ 0.6Yd
Elena	4000	(34000-19000)/20000=0.75	4000+0.75 Yd

The formula for MPC is Slope of the consumption function ie the change in consumption with respect to income.

The calculations are shown in the table above along with MPC and the consumption function.

Consumption function is C0+bY where C0 is the consumption when income is zero ie the autonomous consumption while b is MPC.

b) For finding the aggregate consumption function, we would add the autonomous consumptions of all individuals and the consumption at $20,000 and $40,000

When income is zero, autonomous consumption= 1000+2500+2000+5000+4000=14500$

When income is 20,000, total consumption= 15,000+12500+20000+19000+17000=$83500

When income for one is 20,000, then aggregate income would be 20000*5=$100,000

When income is 40000, total consumption= 29000+22500+38000+29000+34000=$152500

Total income would be 40000*5=200,000

MPC= (152500-83500)/(200000-100000)=69000/100000=0.69

Hence the aggregate consumption function is C=14500+0.69Yd

(You can comment for doubts)