# A firmβs short-run total cost function is ππΆ = π 2 β 3π + 500 The firm is a monopolist and the inverse demand function for its product is π = βπ + 105: Introduction to Mathematical Economics Assignment, UMS, Malaysia

School

###### Universiti Malaysia Sabah (UMS)

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Assignment Type

Subject

Date

###### 17/12/2021

Question 1:

A firmβs short-run total cost function is ππΆ = π 2 β 3π + 500. The firm is a
monopolist and the inverse demand function for its product is π = βπ + 105.

• Β Find the most profitable level of output and the profits at that output.
• Β When maximizing profit, does the firm produce at a minimum average cost?
• Β 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 that 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?

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