Step 1: Understand the characteristics of a purely competitive market. These include many buyers and sellers, homogeneous products, free entry and exit, and perfect information.
Step 2: Analyze each set of markets given in the problem to see if they meet the criteria of pure competition. For example, automobile manufacturing and smartphone production typically have few sellers and product differentiation, so they are not purely competitive.
Step 3: Consider markets like pharmaceuticals, luxury goods, and software development. These often involve product differentiation, patents, or brand loyalty, which means they are not purely competitive.
Step 4: Look at utilities, cable television, and local water supply. These are usually natural monopolies or oligopolies due to high infrastructure costs and limited competition, so they are not purely competitive.
Step 5: Finally, evaluate agricultural products, foreign exchange, and stock exchanges. These markets generally have many participants, standardized products or services, and easy entry and exit, fitting the model of pure competition.