Question

There are three firms in the chert industry. Their demand curves are linear and are given by the following equations.

Q_i= α_i–β_iP_i+ δ_ijP_j+ δ_ikP_k(i,j,k) = (1,2,3).

You are given the following information about these firms.

Firm 1         Firm 2            Firm 3

Prices          35.997          38.779            35.597

Outputs        319.95        175.599          211.94

Gross Margins     .444              .226                .2976

Furthermore, you are given the following diversion ratios:

D₁₂= .25, D₂₁= .20, D₁₃= .25, D₃₁= .40, D₂₃ = .25, D₃₂= .10.

1. Write down the profit maximization conditions for each firm.
2. Using these conditions and the other information given to calculate the unknown demand parameters and the marginal costs.
3. Suppose that Firm 1 and Firm 2 want to merge. You are an analyst at CRAI, a well-known consulting firm. Calculate the UPPI indices for P₁and P₂. Assume 20% cognizable efficiencies.
4. Calculate the post-merger equilibrium prices. Again, assume 20% cognizable efficiencies.

Answer 1

Answer-1. Gross margin= gross margin is the difference between revenue and cost of goods sold divided by revenue.

Revenue-cost of good sold/revenue.

Gross margin is expressed as a percentage.

Net Margin= Net margin or net profit margin is measure of profitability. It is calculated by finding the net profit as a percentage of the revenue.

so we can solve (P-Mc)/P by using net margin because net margin is the real profit after deduction of all cost so deduction of marginal cost which means cost of single product give real value of at which marginal revenue is equals to marginal cost.

Answer-2. Cognizable efficiencies= Cognizable efficiencies defines as the best way to reach profit segment by using different tools like merger is one of them to come out of loss by combining with other company.