1) Aluminium metal is the most electropositive (-1.67V) metal among the listed in the question. It is produced in industry with an electrolysis of a quite complicated melted mixture: alumina, cryolite and calcium fluoride (Hall-Heroult process). Everything is melted at 950-980 C and aluminium is collected (reduced) on the cathode. This requires a large amount of electricity.
2) Iron is less electropositive (-0.44V) metal than aluminium and because of this it could be recovered from its ore with a purely chemical process - reduction with a practically pure carbon. The production process was named Blast Furnace production. Its chemistry consists mainly of three reactions:
2C + O2 = 2CO
Fe2O3 + 3CO = 2Fe + 3CO2
2Fe2O3 + 3C = 4Fe + 3CO2
3) Gold is the most electronegative (+1.50V) and inert metal in the given list. It is on the right side of the reactivity series. However, because of its low reactivity it can be found in a pure state. After gold is separated from the ore it can be refined with Wohlwill or Miller process.
Unfortunately, the reactivity series of these metals and their cost have no direct relation to each other. Aluminium production consumes fantastically huge amount of electricity. In turn, iron or steel requires huge amounts of heat and special sort of refined carbon. They both must be reduced from the ores, which is harder when the metal is more to the left side in the reactivity series. Gold requires no reduction from its ore. It only requires a concentration and a purification. Thus, their cost is mainly dictated with the abundance of those metals in the nature. Aluminium is the most abundant element in the crust and iron is also a highly abundant one. Both form a number of industrially important ores, which can be quite easily found. However, gold is a relatively rare element and this fact dictates its high price together with a historical and economic background.
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