Final answer:
If the clinic signs the contract with a local HMO, its profits will decrease by $12,500 due to a lower price per case despite an increased number of customers.
Step-by-step explanation:
To determine how the clinic's profits will change if it signs a contract with a local HMO for a price of $550 per case and serves 1,250 customers, we must calculate the profits before and after the contract and compare them.
Initially, without the contract, the clinic's profit can be calculated as follows:
Revenue before = Price per case × Number of cases = $600 × 1,000 = $600,000
Total Cost before = Average Cost per case × Number of cases = $400 × 1,000 = $400,000
Profit before = Revenue before - Total Cost before = $600,000 - $400,000 = $200,000
After signing the contract, the clinic's profit changes as follows:
Revenue after = New price per case × New number of cases = $550 × 1,250 = $687,500
Total Cost after = Average Cost per case × New number of cases = $400 × 1,250 = $500,000
Profit after = Revenue after - Total Cost after = $687,500 - $500,000 = $187,500
Therefore, the change in profits = Profit after - Profit before = $187,500 - $200,000 = -$12,500.
The clinic will see a decrease of $12,500 in profits after signing the contract with the local HMO.