Question

The country of Dystopia is composed of 500 workers and 100 managers Workers earn $100 and pay $10 in taxes a day. Managers earn $1,000 a day in salary, bonuses and performance pay. They also own investments that accrue around $300 a day in dividends, interests and capital gains. Managers also pay around $200 a day in taxes. Dystopia provides free health care and housing to all its residents, of $40/day in value Part a) Calculate the net national income of Dystopia. (Assume zero depreciation) Part b) What is the pre-tax labor’s share of national income in Dystopia? Part c) What is the pre-tax share of total income going to the top 20% in Dystopia? Part d) What is the post-tax share of national income going to the top 20% in Dystopia? Part f) Draw the pre- and post-tax Lorenz Curves in Dystopia. Part g) Calculate the pre- and post-tax income Gini coefficients for Dystopia.

Answer 1

a) The formulae for Net National Income is as follows

NNI = C + I + G + NX + NFFI - D - IT

where

NNI = Net National Income, C = Consumption, I = Investment, G = Government Expenditure, NX = Net exports (Exports-Imports), NFFI = Net Foreign Factor Income, D = Depreciation, IT = Indirect Taxes

From the information given in the question, we can figure out the following components and calculate the NNI.

Consumption = number of people*income - direct taxes= 500*$100 + 100*$1,000 - 500*$10 -100*$200= $1,25,000 (as there are 500 workers earning $100 and 100 managers earning $1,000. Also, 500 workers paying $10 tax and 100 managers paying $200 tax) (Assumption is that everything earned is spent)

Investments = 100*$300 = $30,000 (investments of 100 managers)

Government Expenditure = 600*$40 = $24,000 (free health care and housing for all the citizens of Dystopia)

Indirect Taxes = 0 as the taxes in th equestion above seems to be income tax (direct tax)

Depreciation = NFFI = NX = 0 (as no information is available)

Putting in formulae

NNI = $1,25,000+$30,000+$24,000 = $1,79,000

b) Pre tax labour share = (Income earned by each individual before tax)/ National Income

= (500*$100 +100*$1000)/$1,74,000

= $1,50,000/$1,79,000

=83.8% (It does not include investments)

c) There are 600 individuals in Dystopia. 20% of 600 individuals will be top 120 individuals by income.

Thus, the top 20% of income earners = 100 managers + 20 workers ( does not matter which 20 we are selecting as all 500 workers earn the same income)

Pre-tax labor share of top 20% = (Income earned by 120 individuals before tax)/ National Income

= (20*$100 +100*$1000)/$1,74,000

= $1,02,000/$1,79,000

=56.98%

d)  

Post-tax labor share of top 20% = (Income earned by 120 individuals after tax)/ National Income

= (20*$100 +100*$1000 - 20*$10 - 100*$200)/$1,74,000

= $81,800/$1,79,000

=45.69%

As it is not described how many questions I have to answer, I am answering the first four. Please let me know in case you need answers for others as well.