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In economics, the relationship between the price of a commodity and the quantity of that commodity that consumers are willing to purchase is graphically represented by a demand curve. A linear demand curve is a straight line, which is one of the simplest forms you'll encounter in economics. It has the equation of the form y = mx + b, where y represents the quantity demanded, m is the slope of the curve indicating the rate at which quantity demanded changes with price, x represents the price, and b is the y-intercept, indicating the quantity demanded when the price is zero.

The slope is crucial because it tells us how much the demand decreases when the price increases. In the example provided, the demand curve has a negative slope of -13.33, showing us that for each unit increase in price, the quantity demanded decreases by 13.33 units. So, if the price were to decrease, we would expect the demand to go up by the same rate.

The price elasticity of demand measures how much the quantity demanded of a good responds to a change in the price of that good. It provides us with an understanding of how sensitive consumers are to price changes. Elasticity is calculated as the percentage change in quantity demanded divided by the percentage change in price.

• If elasticity is greater than 1, the demand is considered elastic, meaning consumers are highly responsive to price changes.
• If elasticity is less than 1, it's inelastic, and consumers aren't very responsive to price changes.
• If elasticity equals 1, it's unit elastic, meaning consumers respond proportionately to price changes.

For a linear demand curve, the price elasticity of demand changes at different points along the curve. As prices rise and we approach the y-axis, demand becomes more elastic because consumers become more sensitive to further price increases.

Quantity demanded refers to the total amount of a good or service that consumers are willing to purchase at a given price. It is not to be confused with demand itself, which represents the relationship between price and quantity demanded over a range of prices. Understanding the quantity demanded at a specific price can help businesses make decisions about pricing and production.

In the textbook example, we observed how changes in price reflect changes in quantity demanded. When the price was set at \(55, the quantity demanded was 1000 units, and when it increased to \)85, it dropped to 600 units. This concept also ties into 'consumer surplus', which is the difference between what consumers are willing to pay and what they actually pay. By knowing how much quantity demanded changes with the price, businesses can calculate the optimal price to maximize their revenue without losing consumer interest.