Would GDP for a pure endowment economy be equal to zero? (Am I correct?)

As far as I understand, a pure endowment economy means that good just appears in the country without any labor involved in producing them. Like maybe given country lives entirely from aid/gifts/tribute sent from abroad, literally producing nothing of its own (including services).

There are three ways that show that GDP=0

1.GDP stands for Gross Domestic Production. In a pure endowment economy there is no domestic production as such, thus GDP should be equal to zero.

2.We can try to calculate GDP using the income approach. This can result in negative GDP.

GDP=TNI+Sales taxes + Deprecation + NFFI

TNI=Wages + Rent + Interest + Profit

Wages=0 because nobody produces goods (including services!) inside the country.

Profit>=0. There is no profits domestically because nothing is produced domestically, but it's possible for local corporations to get profits aborad.

Interest>=0. Lending money is a service, but there are no local services in our economy, thus no lending to by local lenders to the citizens/firms of the country. But it's possible that local lenders lend their their money abroad.

Rent=0 because renting land is a local service and there are no local services (renting a building isn't an option because nobody builds anything in the country and it's not possible to sent a built building from abroad). So either nobody lends their land OR all lands are common property of all people living inside the country OR property rights over land don't exist as such

Thus TNI>=0. If TNI>0, then TNI+NFFI=0.

Sales Tax=0 because there is no State to collect taxes. And there is no State because any State provices services like the police, the army, the public healthcare, etc. The only way to not have all of these services, is to have NO entity with monopoly on violence, consequently making it impossible to collect taxes. 

Deprecation=0 because businesses would have no capital to deprecate

NFFI=Income of foreigners earned here - Income our citizens earned abroad.

Income of foreigners earned here=0 because Wages,Rent,Interests,Profits=0 domestically (i.e. they can be >0 only if they get money from abroad)

Now it's possible that our citizens earned something abroad, in this case NFFI will become negative, but it will be compensated by equaly-sized positive TNI, consequently making the whole GDP equal to zero.

3.We can caclulate GDP using the expenditures approach.

GDP=Consumption+Investements+Government expenditures+Export-Import

Government expenditures=0 because there is no State.

Consumption=positive number because although there is nothing to buy on the national market it's possible to spend money on imported goods.

Investments=0 because there are no businesses and no new homes to be bought by households.

Export=0 because these are supposed to be goods produced in the country but sold aborad.

Import>0 if our citizens earn money abroad. In this case they can buy goods abroad too and then consume said goods inside the country. This coupled with positive "Consumption" will result in in GDP=0

P.S. From what I read I concluded that the number 1 is incorrect because production of endowment, although happens somehow magically, without any labor of our workers (for an example, it's produced out of the thin air by a magic lamp) is still DOMESTIC production. 

The number 2 is incorrect because it's possible to sell endowments to other citizens and get positive profit as the result  (i.e. domestic profit>0).

The number 3 is incorrect because other citizens would buy (domestically!) endowments owned by other citizens/firms. Thus at the least Consumption would be >0 for domestic goods.
GDP would not be zero in endowment economy in general. There are still prices and also interest rates, savings and investment in endowment economy. First, lets ignore other countries because foreign aid complicates GDP calculations (as Art pointed out if the endowment is foreign aid GDP would be zero). So lets suppose there is only one country, lets call it Arstotzka, which has an endowment economy (i.e. production is fully exogenously given).

A simple macro endowment model of economy would be the following.

There is one representative individual with following utility

$$u = \sum^T_{t=1} u(C_t)$$

where $U$ is the utility, and $C_t$ is a consumption at time $t$. Standard assumptions apply $U'(C_t)&gt; 0, U''(C_t)&lt; 0 $, that is utility is increasing but at decreasing rate.

Now this will be an endowment economy so lets assume initial endowment of $A_0$ and additional per period endowment $Y_t$. 

Logically consumption must be equal or less the endowment, but rational consumers will always use up their whole resources (in this model there is no inheritance) so I can set it as an equality (this just simplifies the math):

$$\sum^T_{t=1} C_t= A_0 + \sum^T_{t=1} Y_t$$

This problem gives us the following lagrangian:

$$\mathcal{L} =  \sum^T_{t=1} u(C_t) + \lambda \left( A_0 + \sum^T_{t=1} Y_t - \sum^T_{t=1} C_t\right) $$

First order conditions are given by:

$$u'(C_t) = \lambda \implies C_1 = C_2 = C_3 =... =C_T $$

This means that the consumption will be same in each period because marginal utility of consumption is constant.

Hence we know consumption will be $C_t = \frac{1}{T}\left( A_0 + \sum^T_{t=1} Y_t \right) $ 

Furthermore, assuming no government and hence no public saving the saving is by definition just difference between endowment income and consumption at time $t$ $S_t = Y_t- C_t$

Now lets parametrize our model. 

Lets suppose we only have two years $t=1,2$. Next the initial endowment is set to 0\$ (to simplify calculations) and the per period endowments are $Y_1 = 60\$ $ and $Y_2= 40\$ $ 

Hence consumption based on the above solution will be $C_1 = 50\$, C_2=50\$$ so in period 1 there is 10 dollars of savings and in period 2 10 dollars of dis-saving $S_1=10\$ $  $S_2=-10\$ $.

Now GDP using consumption approach would be in period 1 $Y = C + I + G = 50 + 10 + 0 = 60 $ (since $I=S$  which is the same which you would get through the income approach as by our set up the endowment in $Y_t = 60\$ $.

To sum it up GDP wont be zero because endowmends are income. In real life on a tax return it would be some windfall profit but regardless thats just semantics. In real life pure endowments dont exist so we dont really have a name for them in accounting formulas but the point of income approach is to add whole income of a nation regardless of how you call the source of income as long as it was produced withing borders of a country for GDP. For expenditure, approach you again just add all spending in an economy again regardless of the fact that spending was based on purchasing some some endowment output $Y_t$ or actually produced through some inputs.