Explain the relationship between the price elasticity of demand and total revenu

Explain the relationship between the price elasticity of demand and total revenue. What are the impacts of various forms of elasticities (elastic, inelastic, unit elastic, etc.) on business decisions and strategies to maximize profit? Explain your responses using empirical examples, formulas, and graphs.
Is the price elasticity of demand or supply more elastic over a shorter or a longer period of time? Why? Give examples.
What are the impacts of government and market imperfections (failures) on the price elasticities of demand and supply?
Please note:
According to the law of demand, if price increases, quantity demanded of a good or service will decrease or vice versa. Price elasticity of demand tells us how much quantity demanded will decrease when price increases or how much quantity demanded will increase if price decreases.
On the other hand, according to the law of supply, if the price increases, quantity supplied of a good or service will increase. Similarly, if price decreases, quantity supplied will decrease. The degree of sensitivity (responsiveness) of production/supply to a change in price is measured by the concept of price elasticity of supply.
Total revenue is calculated as the quantity of a good or service sold multiplied by its market price. Thus, it is a measure of how much money a company makes from selling its product. The core objective of a firm is maximizing profit. One of the ways to maximize profit is increasing total revenue. The firm can increase its total revenue by selling more items or by raising the price. Among others, this depends on the nature of the price elasticity of demand. Moreover, the length of time is an important factor in determining price elasticity of demand and supply.
This paper focuses on readings from: TEXTBOOK FOUND IN FILES
Chapter 4: “Market Failures: Public Goods and Externalities”
Chapter 5: “Government’s Role and Government Failure”
Chapter 6: “Elasticity”
Chapter 7: “Utility Maximization”
Chapter 9: “Businesses and the Costs of Production”
Chapter 10: “Pure Competition in the Short Run”

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