Questions: An industry consists of three firms with sales of 300,000, 700,000, and 250,000. a. Calculate the Herfindahl-Hirschman index (HHI). b. Calculate the four-firm concentration ratio (C4). c. Based on the FTC and DOJ Horizontal Merger Guidelines described in the text, is the Department of Justice likely to attempt to block a horizontal merger between two firms with sales of 300,000 and 250,000?

Let's address each part of the question step by step.

The Herfindahl-Hirschman Index (HHI) is calculated by summing the squares of the market shares of all firms in the industry.

First, we need to determine the market shares of each firm. The total sales of the industry are: \[ \$300,000 + \$700,000 + \$250,000 = \$1,250,000 \]

Now, calculate the market share of each firm:

• Firm 1: \(\frac{\$300,000}{\$1,250,000} = 0.24\)
• Firm 2: \(\frac{\$700,000}{\$1,250,000} = 0.56\)
• Firm 3: \(\frac{\$250,000}{\$1,250,000} = 0.20\)

Next, square each market share and sum them up to get the HHI: \[ HHI = (0.24)^2 + (0.56)^2 + (0.20)^2 \] \[ HHI = 0.0576 + 0.3136 + 0.04 \] \[ HHI = 0.4112 \]

To express the HHI as an integer, multiply by 10,000: \[ HHI = 0.4112 \times 10,000 = 4112 \]

So, the Herfindahl-Hirschman Index (HHI) is: \[ \boxed{4112} \]

The four-firm concentration ratio (\(C_4\)) is the sum of the market shares of the four largest firms in the industry. Since there are only three firms in this industry, we sum the market shares of all three firms:

\[ C_4 = 0.24 + 0.56 + 0.20 = 1.00 \]

Expressed as a percentage: \[ C_4 = 1.00 \times 100 = 100\% \]

So, the four-firm concentration ratio (\(C_4\)) is: \[ \boxed{100\%} \]

To determine if the Department of Justice (DOJ) is likely to block the merger, we need to consider the change in the HHI and the guidelines provided by the FTC and DOJ.

First, calculate the pre-merger HHI, which we already found to be 4112.

Next, calculate the market share of the merged firm:

• Combined sales of the two firms: \$300,000 + \$250,000 = \$550,000
• Market share of the merged firm: \(\frac{\$550,000}{\$1,250,000} = 0.44\)

Now, calculate the new HHI after the merger: \[ HHI_{new} = (0.44)^2 + (0.56)^2 \] \[ HHI_{new} = 0.1936 + 0.3136 \] \[ HHI_{new} = 0.5072 \]

Expressed as an integer: \[ HHI_{new} = 0.5072 \times 10,000 = 5072 \]

The change in HHI due to the merger: \[ \Delta HHI = HHI_{new} - HHI_{old} \] \[ \Delta HHI = 5072 - 4112 = 960 \]

According to the FTC and DOJ Horizontal Merger Guidelines:

• Markets with an HHI above 2500 are considered highly concentrated.
• An increase in HHI of more than 200 points in such markets raises significant competitive concerns.

Since the pre-merger HHI is already above 2500 and the increase in HHI is 960, which is significantly more than 200 points, the DOJ is likely to attempt to block the merger.

So, the answer is: \[ \boxed{Yes} \]