4a. In the market for hand-made guitars, when the price of guitars is $800, annual revenues are $640,000. When the price falls to $700, annual revenues decline to $630,000. Over this range of guitar prices, is the demand for hand-made guitars elastic, unit-elastic, or inelastic? Why? Explain.

4b. Why is the demand for gasoline relatively inelastic, while the demand for Exxon’s gasoline relatively elastic?

4a. Well, the demand for hand-made guitars seems to be inelastic based on the information you've provided. When the price changes from $800 to $700, the quantity demanded only changes from $640,000 to $630,000. This means that the percentage change in price is greater than the percentage change in quantity demanded, indicating inelastic demand. Hand-made guitars must have some magic touch to keep their demand stable even with price fluctuations!

4b. Ah, the wonders of demand elasticity! The demand for gasoline tends to be relatively inelastic because it is a necessity for many people. When the price of gasoline changes, people still need to drive around to work, school, or their favorite clown shows. So, they tend to continue purchasing gasoline at a consistent rate, regardless of the price. However, the demand for Exxon's gasoline specifically may be more elastic because consumers have other options available. They could easily switch to different gas stations or even alternative forms of transportation if Exxon's prices become unfavorable. Variety is the spice of life, after all!

4a. To determine the elasticity of demand for hand-made guitars, we need to calculate the price elasticity of demand (PED) using the formula:

PED = (% Change in Quantity Demanded) / (% Change in Price)

First, let's calculate the percentage change in quantity demanded:

% Change in Quantity Demanded = (New Quantity Demanded - Original Quantity Demanded) / (Original Quantity Demanded) * 100

% Change in Quantity Demanded = (630,000 - 640,000) / 640,000 * 100
% Change in Quantity Demanded = -1.5625%

Next, let's calculate the percentage change in price:

% Change in Price = (New Price - Original Price) / (Original Price) * 100

% Change in Price = (700 - 800) / 800 * 100
% Change in Price = -12.5%

Now, we can substitute these values into the price elasticity of demand formula:

PED = (-1.5625% / -12.5%) = 0.125

Since the absolute value of the price elasticity of demand is less than 1 (0.125 < 1), the demand for hand-made guitars in this price range is inelastic. This means that a change in price does not lead to a proportionally large change in quantity demanded.

4b. The demand for gasoline is relatively inelastic because it is considered a necessity for many people. Even if the price of gasoline increases, people still need to purchase it for transportation purposes, and thus, the quantity demanded does not decrease significantly.

On the other hand, the demand for Exxon's gasoline may be relatively elastic because there are alternative options available in the market. Consumers have the choice to buy gasoline from other companies, and they can switch to those alternatives if Exxon's prices are too high. Therefore, a change in price by Exxon may result in a larger change in quantity demanded due to the availability of substitutes.

To determine whether the demand for hand-made guitars in this scenario is elastic, unit-elastic, or inelastic, we can calculate the price elasticity of demand. Price elasticity of demand measures the responsiveness of the quantity demanded to a change in price.

To calculate the price elasticity of demand, we use the following formula:

Elasticity = (Percent change in quantity demanded / Percent change in price)

Let's calculate the percent change in quantity demanded first:

Percent change in quantity demanded = [(New quantity demanded - Old quantity demanded) / Old quantity demanded] x 100

The new quantity demanded is 630,000 guitars, and the old quantity demanded is 640,000 guitars.

Percent change in quantity demanded = [(630,000 - 640,000) / 640,000] x 100 = (-10,000 / 640,000) x 100 = -1.56%

Next, let's calculate the percent change in price:

Percent change in price = [(New price - Old price) / Old price] x 100

The new price is $700, and the old price is $800.

Percent change in price = [(700 - 800) / 800] x 100 = (-100 / 800) x 100 = -12.5%

Now, we can calculate the price elasticity of demand by using the formula mentioned earlier:

Elasticity = (-1.56% / -12.5%)

Elasticity = 0.125

In this case, the price elasticity of demand is positive and less than 1, indicating that demand for hand-made guitars is inelastic. An inelastic demand means that the change in quantity demanded is less responsive to changes in price. In this scenario, as the price of guitars fell from $800 to $700, the decrease in revenue was relatively small (from $640,000 to $630,000), indicating that demand did not decrease significantly.

Moving on to the second part of the question, the demand for gasoline is relatively inelastic while the demand for Exxon's gasoline is relatively elastic. This is because the availability of substitutes plays a crucial role in determining the elasticities of demand.

The demand for gasoline, in general, tends to be inelastic because there are limited substitutes. People largely rely on gasoline for transportation, and there are limited alternative energy sources available for widespread adoption. As a result, even if the price of gasoline increases, people are generally not able to reduce their demand significantly due to the lack of suitable alternatives.

On the other hand, the demand for Exxon's gasoline specifically might be relatively elastic because there are other gasoline brands available as substitutes. If Exxon raises its prices significantly, consumers can switch to other gasoline brands without much inconvenience. Therefore, consumers are more likely to be responsive to price changes for Exxon's gasoline compared to the general gasoline market, making demand relatively more elastic.