The points (1) to (4) are meant to be in ascending order of complexity.
This means you start with a relatively simple economy in (1), (2) extends (1),
(3) extends the (2) economy, and (4) extends the (3) economy. Note that (5)
extends (3), and here the extension in (4) can be ignored.

1. We start from the model economy introduced by Ana Ania-Martinez.
There are two firms A and B. Firm A produces steel and sells it for a
basic price of 100 e plus 10% value added tax (VAT) to firm B. Firm B
uses steel as its input to produce three cars at a basic price of 70 e each
and sells them including 20% VAT to domestic consumer households. Firm
A pays wages to its employees of 80 e and thus faces profits (operating
surplus) of 20 e. Firm B is owned by the households. It pays 70 e of
wages and also transfers the 40 e of its operating surplus to its own-
ers. Firm A is owned by foreigners, so the 20 e of profits are transferred
abroad. Households have an additional wage income of 50 e from the
rest-of-the-world. We know that gross domestic product (GDP) is 252 e
(it includes VAT), and that gross national income (GNI) is 282 e (note
that Ana’s page 5 does not account for taxes, which explains the slight
discrepancy to her figures; also we do not have any depreciation here,
see point # 4 for that). As in all following points, check the account 0
identity GDP = C + I + G + X − IM by determining all components
and the saving identity I = SH + SF + SP + SRoW. Note that I = 0,
so saving components must add to zero likewise. Also determine personaldisposable income, which is the households’ disposable income, i.e. their
income minus possible taxes. Here, households do not face direct taxes,
so their disposable income is just the sum of all wage incomes plus firm
B’s profits.

2. Due to their recognizable negative saving, households (who own firm B)
decide to use the 40 e of car manufacturer’s profits to invest. This invest-
ment is easily implemented, as they just have to forego buying one of the
three cars for household pleasure. They rather retain this car within firm
B, and it becomes part of the capital stock. The government supports this
activity by a subsidy: for the unsold car, no VAT needs to be remitted.
Then, investment I is the value of a ‘business car’ at market prices, i.e.
70e. Again, check the account 0 identity and the saving identity. Take
care. Household saving has increased, as the expenses for a car exceed
the foregone profits. Firm saving has increased to the market value of
a car, now an asset, minus the loss implied by sales minus expenses on
taxes, wages, and intermediate goods. Also determine the (now smaller)
personal disposable income. Production has not changed, while GDP has
decreased by the lower taxation on cars.

3. In order to entertain the hard-working households, government decides to
do something with their surplus. They use their revenues of 28e to pay a
troupe of clowns and jugglers from the neighboring economy, who perform
on a regular basis free of charge but do not become residents. This means
we now have imports of services and production of a public good. While
28e cross the border out, GDP will increase for the following reason. A
public good is produced at a value of 28e at basic prices but at more than
that at imputed market prices. While government will not pay taxes to
themselves, we impute the market value of the performance at 33e. GDP
has increased by 5e of non-existing VAT. Again, evaluate the account 0
identity and the saving identity. Note that government saving is now 0,
which is compensated by the saving of RoW. Determine GNI and GDP.
Also note that government spending is measured at market value inclusive
of VAT, while imports are measured at the net value of 28e.

4. Cars depreciate fast. For this reason, assume that the depreciation rate
for a new car is 20%. Determine net domestic product and net national
income. Note that the depreciation does not affect the households: a
private car is just a consumer good and its loss of value does not show in
the main accounts. By contrast, a business car is an investment good.

5. Suppose government increases its revenues by taxing profits at 10%, while
wages remain untaxed. Firm B is exempt from such taxes, as it can
show that it uses its profits for investment. Firm A, however, is taxed.
Determine how this change affects the saving identity and GNI. Note that
GDP and the account 0 identity are unaffected, as income taxes are mere
transfers and do not modify the value of production.