1) This is a large topic. I will start off with a basic approach:

The Gemara here (44b) states that the reason why a silver Machtah was used every day to scoop the coals is because of "ha'Torah Chasah...." Rashi (DH Chasah) writes that when one scoops coals, this wears away the Kli and makes it thinner. The Ritva cites Rashi and adds that in such a way one cannot say that one is contradicting the rule of Ein Aniyus b'Makom Ashirus. The Ritva does not explain why using a silver coal-pan is not considered poverty if one could use a gold pan.

I want to suggest an explanation based on what the Perush ha'Ra'avad on Maseches Tamid (29a, printed at the back of Maseches Tamid, after the end of the Masechta) writes: to use a silver vessel is not considered as acting like a pauper, even though one could have used a gold one. It is only considered Aniyus if one uses a wooden or copper vessel.

2) Above I gave an explanation for why the Machtah does not have to be gold, and now I will try to show why the Kalpi is made out of wood.

a) This is discussed in a Teshuvah in the Sefer Teshuva me'Ahavah 1:7, by Rav Elazar Flekles, a close Talmid of Rav Yechezkel Landau, the author of the Noda b'Yehudah. That Teshuvah (1:7) is actually a Teshuvah written by the Noda b'Yehudah himself to his student.

The Noda b'Yehudah writes that if it is essentiaL for something to be done in a Kli Shares, then we say Ein Aniyus b'Makom Ashirus. This rule fits in well with the Gemara in Yoma 39a, where Rava says that the Kalpi was made out of wood and was "Chol" -- it did not possess Kedushah. Ravina asks, "Why do we not make the Kalpi Kodesh?" and Rava answers that if we would be Makdish it, this would mean that it is a Kli Shares, and the Halachah is that one does not make a Kil Shares out of wood. The Gemara then asks that we should make the Kalpi from gold or silver, and the Gemara answers, "ha'Torah Chasah Al Mamonan Shel Yisrael." This suggests that we only say "ha'Torah Chasah" if it is not a Kli Shares, but if it would be a Kli Shares we would say "Ein Aniyus b'Makom Ashirus."

b) I found, bs'd, that the Teshuvah me'Ahavah 2:293 cites somebody who questioned the Noda b'Yehudah from Maseches Tamid 29a, which says that they used a golden vessel to give a drink to the animal that was going to be offered as the Korban Tamid. The Gemara there states that the reason for the gold cup is "Ein Aniyus b'Makom Ashirus." The Teshuvah me'Ahavah agrees that the gold cup is not a Kli Shares, so he concludes that Tamid 29a does indeed contradict his teacher, the Noda b'Yehudah.

c) However, I found, bs'd, that Rashi (Me'ilah 19b, DH Hu Atzmo) writes that the gold cup is an example of a Kli Shares. According to this, the Noda b'Yehudah's rule stands firm.

3) The Tiferes Yisrael says that it depends on how much money the Beis ha'Mikdash is losing:

a) I found, bs'd, that the Tiferes Yisrael (Maseches Shekalim 8:3 in Boaz) writes that the rule of "Ein Aniyus..." means that sometimes we do not concern ourselves with "Harvachah d'Hekdesh" -- that the Beis ha'Mikdash should make a profit. He cites Kesuvos 107a (which I suspect is a printing error and should read either Kesuvos 106a or 106b), where the Gemara cites many different examples of people doing holy jobs in the Beis ha'Mikdash, who receive their salaries from the Beis ha'Mikdash funds. So even though, generally speaking, we have a rule that "Yad Hekdesh Al ha'Elyonah" (the Beis ha'Mikdash has the upper hand in monetary doubts; see Bava Metzia 55a), sometimes we say the opposite -- that the Beis ha'Mikdash should spend its money generously.

b) The Tiferes Yisrael gives another possible explanation of "Ein Aniyus...": We are not concerned about the Beis ha'Mikdash suffering a Hefsed Mu'at, a small loss. He cites Menachos 88b, where we learn that the mouth of the candles of the Menorah should also be made out of pure gold. The Gemara says that one might have thought that since the gold there will become blackened, we should make them out of a lower quality of gold because of the rule "ha'Torah Chasah...," and thus we need to be told that they must be made of pure gold. The Tiferes Yisrael writes that the conclusion of the Gemara there is "Ein Aniyus..." since only a small loss is involved in using pure gold rather than standard gold.

4) There seem to be two places in the Gemara where the opinions "Ein Aniyus" and "ha'Torah Chasah" are presented as a Machlokes:

a) The Gemara in Menachos (end of 89a) states that the Menorah in the Beis ha'Mikdash must be alight from the evening until the following morning. The Gemara states that the Chachamim estimated that half a Lug of oil is required to keep the candles of the Menorah alight. The question is now asked, how did the Chachamim carry out the experiment to estimate how much oil is needed? One opinion states that they went "from up downwards" and the other opinion holds that they went "from down upwards." This means that the first opinion says that on the first night they put in a Lug of oil and in the morning they found that oil was left over because they had put in more than was necessary. They discarded the extra oil, and on the second night they put in less than a Lug until they eventually came to the conclusion that no more than half a Lug is needed. The second opinion holds that they performed the experiment the other way around. On the first night they put in a quarter of a Lug and saw that this was not sufficient. On the second night they put in more until they eventually came to the conclusion that half a Lug is required.

The Gemara concludes that the first opinion holds "Ein Aniyus." We do not want that on any night there should not be enough oil to last to the next morning, since it is only poor men who cannot afford to burn a candle until the next morning. The second opinion maintains that "ha'Torah Chasah." We never want to get to a situation where he have to throw out oil donated to the Beis ha'Mikdash since the Torah tries to save people's money.

The simple meaning of this Sugya would be that "Ein Aniyus" and "ha'Torah Chasah" are two diametrically opposed ideas.

b) The other Gemara is in Tamid 29a. The Gemara there cites the Mishnah (Tamid 30a) which teaches that the animal of the Korban Tamid was given to drink in a gold cup. Rava said that this is an exageration. They did not really give an animal a drink in a gold cup. This is because Rava holds that "ha'Torah Chasah" (see Sefer Esh Das on Parshas Beha'aloscha, DH v'Efshar, by Rav Chaim Alfandri). But Rav Yanai bar Nachmani there disagrees with Rava and says that they literally gave the animal to drink from a gold cup. The Gemara there states explicitly that this is because Rav Yanai holds that "Ein Aniyus"

5) To conclude this topic (which is in fact a very broad one, with many sources in Shas and much discussion in the Mefarshim; I have really only attempted to give a taste of the Sugya), let us ask: Is it really true that "Ein Aniyus" and "ha'Torah Chasah" are two opposing opinions in Chazal? Let us see a major Acharon who says that it all depends on the judgement of the Chachamim, when to be more generous and when to be more economical:

a) The Sefer Yom Teru'ah by Maharam Chaviv (who lived about 350 years ago, and who is cited in this Sugya by a number of later Acharonim, including the Sedei Chemed, Ma'areches Alef, #128), on Rosh Hashanah 27a (end of DH M"SH Hasam d'Zahav), discusses the Sugya about the mouthpiece of the Shofar used on Rosh Hashanah in the Beis ha'Mikdash being gold-plated and the one used on fast days being silver-plated. He asks: Why, in Kesuvos 106b do we learn that one may not make a profit out of Hekdesh because of the rule "Ein Aniyus," while in Rosh Hashanah 27a we use the rule "ha'Torah Chasah" to explain why the fast day Shofar is only silver plated?

b) The Yom Teru'ah answers that both rules are true sometimes and which one we employ depends on the circumstances. Sometimes one has to open one's hand generously and give because of "Ein Aniyus." Sometimes one has to be careful how much one spends because of "ha'Torah Chasah." The Yom Teru'ah writes that it depends on the way that the Chachamim weighed their judgement to distinguish between one scenario and another.

c) I suggest that according to this approach, we have a way of understanding the dispute about how we do the experiment to decide how much oil to put into the lamps. One opinion maintains that it is not correct to do this test when we know that some oil will actually be discarded. The other opinion says that this is a one-time test, and it is correct to waste a small amount of oil to avoid ever having a situation where the candle does not burn all night.

Similarly, Rava says that it is an exaggerated practice to give an animal to drink in a gold cup. Rav Yanai says that the honor and glory of the Beis ha'Mikdash is more important than the possibility that people may laugh at an animal drinking from a gold cup. Neither the Gemara in Menachos 89b or the Gemara in Tamid 29a is saying that there is a general dispute about "ha'Torah Chasah" or "Ein Aniyus." Rather, the question is in each individual case, how do weigh the advantages of being generous against the disadvantages?

I think that the guidelines of the Maharam Chaviv can help us with a number of riddles in the Sugya, but I must close now.

Dovid Bloom