Answer:

Maximising Profit with Fixed Price Output

The objective of this problem is to find the values of the parameters 𝛼 and 𝛽 that satisfy the second order conditions for maximising profit when the output of the company is sold at a fixed price 𝑝. The output is given by the equation 𝑞 = min (𝑧1^(𝛼) ,𝛽𝑧2 ).

Second Order Conditions

The second order conditions for maximising profit are derived by taking the first and second derivatives of the profit function. The first order conditions give the values for 𝛼 and 𝛽 that maximise profit. The second order conditions indicate whether the profit function is at a maximum or a minimum.

Finding the Parameter Values

In order to calculate the parameter values 𝛼 and 𝛽 that satisfy the second order conditions for maximising profit, the derivatives of the profit function must be calculated and then set equal to zero. After solving for the parameter values, the second order conditions can be evaluated to determine if the profit function is at a maximum or a minimum.

Conclusion

In conclusion, the values of the parameters 𝛼 and 𝛽 that satisfy the second order conditions for maximising profit when the output of the company is sold at a fixed price 𝑝 can be found by taking the derivatives of the profit function and setting them equal to zero.

Related Questions

  • How do the first order conditions help to maximise profit?
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  • How do you calculate the derivatives of a profit function?
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