This problem tests your understanding of the effect of the income distribution o

ID: 1172961 • Letter: T

Question

This problem tests your understanding of the effect of the income distribution on savings rates.

The economy of Sonrisa has 1000 people in three income categories: poor, middle class, and rich. The

poor ear $500 per year and have to spend it all to meet their consumption needs. The middle class earn

$2,000 per year, of which $1,500 is spent and the rest saved. The rich earn $10,000 per year, and consume

80% of it, saving the rest.

(a) Calculate the overall saving rate in Sonrisa if 20% of the people are poor and 50% are in the middle

class.

(b) Suppose that all growth occurs by moving people from the poor category to the middle-class category

(all poor people become middle-class people). Will the saving rate rise over time or fall?

that in (b): all middle-class people become poor.

a) Total Income of Sonrisa=200*500+500*2000+300*10000=$4.1million

Total saving=200*0+500*500+300*2000=$0.85million

%Saving=Total Saving/Total Income=0.85/4.1=20.73%

b) Say x people moved from poor to middle

Total Income of Sonrisa=(200-x)*500+(500+x)*2000+300*10000=$4.1million+1500x

Total saving=(200-x)*0+(500+x)*500+300*2000=$0.85million+500x

Saving rate=0.85+500x/4.1+1500x

Differentiating

500*(4.1+1500x)-1500*(0.85+500x)=1.55

Therefore slope is positive so saving rate will increase over time

c) Say x people moved from middle to poor

Total Income of Sonrisa=(200+x)*500+(500-x)*2000+300*10000=$4.1million-1500x

Total saving=(200+x)*0+(500-x)*500+300*2000=$0.85million-500x

Saving rate=0.85-500x/4.1-1500x

Differentiating

-500*(4.1-1500x)+1500*(0.85-500x)=-1.55

Therefore slope is negative so saving rate will decrease over time

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