Microbial pigments are colored compounds produced by microorganisms (bacteria, fungi, algae, yeasts). Some of these have industrial applications, for example, as food colorants, in cosmetics, or for pharmaceutical purposes.
Let's analyze the options:
(a) Chlorophyll: The primary photosynthetic pigment in plants, algae, and cyanobacteria. While produced by microbes (algae, cyanobacteria), its large-scale industrial extraction is often from plants. It is used as a food colorant (E140). This is a plausible microbial pigment with industrial use.
(b) Melanin: A pigment found in animals (including humans, responsible for skin, hair, eye color) and also produced by some fungi and bacteria. It has potential applications in cosmetics (UV protection) and biomedicine, but widespread industrial use as a "pigment" for coloration might be less common than others.
(c) Carotene (\(\beta\)-carotene): Carotenoids are a large class of pigments. \(\beta\)-carotene is produced by various microorganisms, including the alga Dunaliella salina and the fungus Blakeslea trispora, as well as by plants. It is widely used industrially as a food colorant (E160a), a feed additive (for animal coloration), and as a provitamin A source. This is a very strong candidate.
(d) Hemoglobin: The iron-containing oxygen-transport protein in red blood cells of vertebrates and some invertebrates. It is not typically considered a "microbial pigment" for industrial applications in the same way as colorants.
Considering "microbial pigment used in industrial applications" specifically for coloration or as a product:
\(\beta\)-carotene (a type of carotene) is a very prominent example of a microbial pigment with significant industrial use as a colorant and nutritional supplement. Chlorophyll from microbial sources (like algae) is also used.
Between chlorophyll and carotene, \(\beta\)-carotene produced microbially (e.g., by Dunaliella) is a major industrial product.
The question asks for "an example". Both (a) and (c) could fit from microbial sources.
However, "Carotene" (specifically \(\beta\)-carotene) is a very well-established example of a microbial pigment with large-scale industrial production and application as a food colorant and vitamin precursor.
If only one is to be chosen, Carotene is an excellent example.
\[ \boxed{\text{Carotene}} \]