To evaluate market power within an industry, one effective method is the four-firm concentration ratio (CR4). This ratio provides insight into how much output is controlled by the largest firms in the market. The calculation involves two main steps: first, determining the total industry output, and second, identifying the output of the top four firms.
To find the total industry output, sum the outputs of all firms in the industry. For example, if the outputs of various saxophone players are 350, 100, 50, 220, 80, 60, 300, and 1, the total output can be calculated as follows:
$$\text{Total Output} = 350 + 100 + 50 + 220 + 80 + 60 + 300 + 1 = 1161$$
Next, identify the four firms with the largest outputs. In this case, the top four outputs are 350 (John Coltrane), 300 (Bradford Marsalis), 220 (Cannonball Adderley), and 100 (Charlie Parker). The output of these four firms is calculated by adding their individual outputs:
$$\text{Output of Top 4 Firms} = 350 + 300 + 220 + 100 = 970$$
Finally, the four-firm concentration ratio is determined by dividing the total output of the top four firms by the total industry output:
$$\text{CR4} = \frac{\text{Output of Top 4 Firms}}{\text{Total Industry Output}} = \frac{970}{1161} \approx 0.836 \text{ or } 83.6\%$$
This result indicates that the four largest firms account for approximately 83.6% of the total output in the industry, suggesting a high level of concentration and market power among these firms. A higher concentration ratio typically implies less competition and greater market control by the leading firms.