Do you think that the dairy industry is an example of a purely competitive market?

Normally purely competitive markets are luxuries. Dairy is necessary for children and adults to get their daily calcium and vitamin d (among other things). In the current market, families can choose vegan, vegetarian, or non-lactose choices for milk, ice cream, etc. Essentially this product is regulated by the government and maintains a low cost even when other "necessary" items go up.

Jmo