1)QUESTION 1

A monopolistic producer of two goods has a total cost function =51+102. Meanwhile, the demand equations are 1=5012 and 2=100142.

i) Calculate the values of 1 and 2 will yield a maximum profit.

(6 marks)

ii) Using the Hessian, prove that the firm's profit is at a maximum.

(6 marks)

2)QUESTION 2

Using the same given functions in QUESTION 1, now consider if the firm's total costs are fixed at RM100.

i) Calculate once again the values of 1 and 2 will yield a maximum profit.

(6 marks)

ii) Calculate the optimal profit.

(3 marks)

iii) Using the bordered Hessian, prove that the firm's profit is at a maximum.

(7 marks)

iv) Estimate the new optimal profit if total costs rise to RM102.