WHY WHEN WE ARE ON THE DOWNWARD SLOPING SIDE OF THE LAFFER CURVE WOULD A TAX CUT GIVE PEOPLE AN INCENTIVE TO WORK MORE AND JOIN THE LABOR FORCE?I...

Laffer curve, named after economist Arthur Laffer is a
graph of tax rate expressed as a percentage of income versus the total tax revenue.
Please note that the shape of Laffer curve does not determine the behavior of people.
Rather Laffer curve depends on behavior of people.

As
represented by Laffer curve, total revenue initially rises as the tax rate are increase
from a level of 0 % or no tax, reaches a maximum level of total revenue, and then again
declines to reach a level of 0 revenue at the tax rate of 100
percent.

The typical shape of Laffer curve is because of
two factors that contribute to the total revenue. We
know:

Total revenue = Total income x Tax
rate

When the tax rate is low the people retain most of the
amount they earn and therefor have greater motivation to increase their earnings, and as
the tax rate increases they have reduced motivation to earn. leading to reducing total
income as the tax rate rises. Thus tax revenue is a product of two variables, total
income and tax rate. The total income falls as the tax rate increases reaching to a
level of 0 when ax rate is 100%. The tax revenue is thus 0 when either the tax rate or
total income is 0. Therefor the tax revenue is 0 when the tax rate is either 0 or 100%.
In between these two points the tax revenue reaches a maximum level as the rise in tax
is accompanied with less matching fall in total income. The total revenue levels of to a
maximum level at point where rise in tax is accompanied by matching  fall in total
income. After this point the rise in tax is accompanied with more than matching  fall in
total income, resulting in falling tax revenue.