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Consider the following Total Revenue (TR) and Total Cost (TC) functions for a firm operating in a perfect competition market: TR = 6Q and TC = Q3 – 2Q2 + 50Q + 25 A) Determine the profit maximizing or loss minimizing equilibrium level of output

Answer:

The Profit Maximizing or Loss Minimizing Equilibrium Level of Output

The profit maximizing or loss minimizing equilibrium level of output can be determined by examining the Total Revenue (TR) and Total Cost (TC) functions for a firm operating in a perfect competition market. In this case, the Total Revenue is 6Q, and the Total Cost is Q³ – 2Q² + 50Q + 25.

Calculating the Profit Function

The profit maximizing or loss minimizing equilibrium level of output can be calculated by subtracting the Total Cost from the Total Revenue, and then finding the maximum of the resulting Profit Function. The Profit Function for this example can be calculated as 6Q – (Q³ – 2Q² + 50Q + 25).

Finding the Maximum of the Profit Function

The maximum of the profit function can be determined by finding the derivative of the profit function, setting the derivative to zero, and then solving for Q. The derivative of the Profit Function is 6 – 3Q² + 4Q, which when set to zero and solved for Q results in Q = 0 and Q = 4.

Calculating the Maximum Profit

The maximum profit can be calculated by substituting Q = 0 and Q = 4 into the Profit Function and then comparing the results. When Q = 0, the Profit Function results in -25, and when Q = 4, the Profit Function results in 10. Therefore, the maximum profit occurs when Q = 4.

Conclusion

In conclusion, the profit maximizing or loss minimizing equilibrium level of output for the given Total Revenue and Total Cost functions is 4.

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