Let's break down each part of the question to understand the key concepts and what is being asked for.

Step 1: Calculate Total Revenue at Various Prices on the Initial Graph

The demand curve shows the relationship between the price of bippitybops and the quantity demanded. Total Revenue (TR) is calculated using:

$TR = \text{Price} \times \text{Quantity}$

For each price point along the demand curve, calculate the total revenue. Let's assume the table contains price points such as $30, $45, $60, $75, etc. You can place a green point on the graph for each calculation based on the data provided.

Step 2: Plot Annual Total Revenue

Once you've calculated the total revenue at each price point, plot those points on the second graph. You can see the general behavior of the total revenue curve—whether it is increasing, decreasing, or reaching a maximum value.

Step 3: Midpoint Method to Calculate Price Elasticity of Demand (Between Points A and B)

The price elasticity of demand (PED) between two points measures how sensitive the quantity demanded is to a change in price. Using the midpoint formula:

$PED = \frac{ \frac{\Delta Q}{\left(Q_1 + Q_2\right)/2} }{ \frac{\Delta P}{\left(P_1 + P_2\right)/2} }$

Where:

• $\Delta Q$ is the change in quantity demanded,
• $Q_1$ and $Q_2$ are the initial and final quantities,
• $\Delta P$ is the change in price,
• $P_1$ and $P_2$ are the initial and final prices.

You can plug in the values for points A and B from the initial demand curve to calculate the price elasticity of demand.

Step 4: Effect of a $15 Price Increase on Total Revenue

Once you have the price elasticity of demand, you can determine the effect of a $15-per-bippitybop increase on total revenue. If the demand is elastic (PED > 1), a price increase will decrease total revenue. If the demand is inelastic (PED < 1), a price increase will increase total revenue.

Step 5: Conditions for Price Decreases Leading to Revenue Decreases

If a price decrease leads to a decrease in total revenue, the demand must be inelastic. This means that the percentage change in quantity demanded is smaller than the percentage change in price.

Summary

• Total revenue is calculated as price multiplied by quantity.
• The price elasticity of demand (PED) determines how sensitive the quantity demanded is to price changes.
• If demand is elastic, a price increase will lead to lower total revenue.
• If demand is inelastic, a price increase will increase total revenue.

Do you need further details on any of these points? Here are some related questions:

1. How do you interpret the shape of the total revenue curve?
2. What is the relationship between elasticity and total revenue at different points on the demand curve?
3. Can price elasticity of demand change at different price ranges?
4. How does unitary elasticity (PED = 1) affect total revenue?
5. What other factors, apart from price, can influence the demand for bippitybops?

Tip: Elasticity can be different at various price levels—elastic at one point and inelastic at another. Analyze carefully.