A firm’s short-run total cost function is 𝑇𝐶 = 𝑞 2 − 3𝑞 + 500 The firm is a monopolist and the inverse demand function for its product is 𝑝 = −𝑞 + 105: Introduction to Mathematical Economics Assignment, UMS, Malaysia

Question 1:

A firm’s short-run total cost function is 𝑇𝐶 = 𝑞 2 − 3𝑞 + 500. The firm is a
monopolist and the inverse demand function for its product is 𝑝 = −𝑞 + 105.

•  Find the most profitable level of output and the profits at that output.
•  When maximizing profit, does the firm produce at minimum average cost?
•  Sketch the graphs of the inverse demand function, marginal revenue function, and marginal cost function with the same axes, showing the equilibrium price, MR and MC, and output.
• Sketch the graphs of total cost and total revenue with the same axes, showing the equilibrium output and profits.

Question 2:

A firm owns a machine which when new produces annual outputs worth RM100,000.00. However, as the machine gets older its productivity falls due to wear and tear, and after 5 years its annual output will be worth only RM20,000.00. What is the average annual rate of depreciation?