Suppose in an economy the income from the private sector is $$\$ 1,550$$ million. The government in this country may choose either to levy a \(5 \%\) sales tax or to levy an income tax to finance its expenditures. It balances its budget. What is the National Product of this economy, its National Income, and its Disposable Income under both proposed tax systems?

Under the 5% sales tax system, the National Product (NP) can be calculated using the given private sector income and the equation \(1,550 = 0.95 * NP\). Solving for NP, we find that the National Product is \(1,631.58 million\). Since there is no income tax, the Disposable Income is equal to the National Income, which is also \(1,631.58 million\). In the case of the income tax system, the National Product is equal to the private sector income plus government expenditures. We also know that the tax revenue is equal to the income tax rate multiplied by the National Income (NI). By setting up the equations and plugging in the values, it will be possible to determine the values of NP and Disposable Income under this tax system. In conclusion, the National Product, National Income, and Disposable Income under the two tax systems can be calculated using the given information and equations. The 5% sales tax system results in \(1,631.58 million\) for both the National Product and Disposable Income. The income tax system requires further calculations to determine these values.