Why would a government stimulus have a multiplier effect on the economy?

A government stimulus would have a multiplier effect on
the economy because the money that the government spends on the stimulus would be spent
over and over again by various people in the economy.  In that way, economic activity
would increase by much more than the amount that the government
spent.

Imagine, for example, that the government pays you
$10,000 for your part in a new construction project.  We'll say you save $1,000 and
spend the other $9,000 to buy various things that you need.  When you spend the $9,000
the owner of the store where you spent it will take that $9,000 and spend perhaps $8,000
of it.  Now, you can already see the multiplier at work.  The government has spent
$10,000 in stimulus money and economic activity has already increased by $17,000 (the
$9,000 you spent and the $8,000 the storeowner spent).  If this process keeps happening,
the multiplier rises.