Question

Answer the following questions concerning the demand schedule below. a. Complete the total-revenue, margina-revenue, and average-revenue data: $$ \begin{array}{|c|c|c|c|c|} \hline \text { Price } & \text { Quantity } & \text { Total } & \text { Marginal } & \text { Average } \\ \hline 20 & 2 & 40 & +17 & 20 \\ \hline 19 & 3 & 57 & +15 & 19 \\ \hline 18 & 4 & 72 & & 18 \\ \hline 17 & 5 & \- & \- & \- \\ \hline 16 & 6 & \- & \- & \- \\ \hline 15 & 7 & \- & \- & \- \\ \hline 14 & 8 & \- & \- & \- \\ \hline 13 & 9 & \- & \- & \- \\ \hline 12 & 10 & \- & \- & \- \\ \hline 11 & 11 & \- & \- & \- \\ \hline 10 & 12 & \- & \- & \- \\ \hline 9 & 13 & \- & \- & \- \\ \hline \end{array} $$ b. What happens to the difference between selling price and marginal revenue?

Short answer

The completed table is as follows: $$ \begin{array}{|c|c|c|c|c|} \hline \text { Price } & \text { Quantity } & \text { Total } & \text { Marginal } & \text { Average } \\ \hline 20 & 2 & 40 & +17 & 20 \\ \hline 19 & 3 & 57 & +15 & 19 \\ \hline 18 & 4 & 72 & +13 & 18 \\ \hline 17 & 5 & 85 & +11 & 17 \\ \hline 16 & 6 & 96 & +9 & 16 \\ \hline 15 & 7 & 105 & +7 & 15 \\ \hline 14 & 8 & 112 & +5 & 14 \\ \hline 13 & 9 & 117 & +3 & 13 \\ \hline 12 & 10 & 120 & +1 & 12 \\ \hline 11 & 11 & 121 & -1 & 11 \\ \hline 10 & 12 & 120 & -3 & 10 \\ \hline 9 & 13 & 117 & -5 & 9 \\ \hline \end{array} $$ As the selling price decreases, the difference between the selling price and marginal revenue decreases. The marginal revenue decreases at a faster rate than the selling price, causing the gap to narrow and eventually become negative.

Step-by-step solution

Calculating Total Revenue for the Given Prices and Quantities

For each given price and quantity, we can calculate the total revenue by multiplying the price by the quantity. For the first two provided entries in the table, the total revenues are: Total Revenue at Price 20: 20 * 2 = 40 Total Revenue at Price 19: 19 * 3 = 57 We now continue in the same way for the remaining prices and quantities: Total Revenue at Price 18: 18 * 4 = 72 Total Revenue at Price 17: 17 * 5 = 85 Total Revenue at Price 16: 16 * 6 = 96 Total Revenue at Price 15: 15 * 7 = 105 Total Revenue at Price 14: 14 * 8 = 112 Total Revenue at Price 13: 13 * 9 = 117 Total Revenue at Price 12: 12 * 10 = 120 Total Revenue at Price 11: 11 * 11 = 121 Total Revenue at Price 10: 10 * 12 = 120 Total Revenue at Price 9: 9 * 13 = 117

Calculating Marginal Revenue for the Given Quantities

To calculate marginal revenue, find the difference in total revenue and divide it by the difference in quantity. For example, using the first two provided entries in the table: Marginal Revenue between Prices 20 and 19: (57 - 40) / (3 - 2) = 17 To find the marginal revenues for the remaining quantities, repeat this process: Marginal Revenue between 4 and 3: (72 - 57) / (4 - 3) = 15 Marginal Revenue between 5 and 4: (85 - 72) / (5 - 4) = 13 Marginal Revenue between 6 and 5: (96 - 85) / (6 - 5) = 11 Marginal Revenue between 7 and 6: (105 - 96) / (7 - 6) = 9 Marginal Revenue between 8 and 7: (112 - 105) / (8 - 7) = 7 Marginal Revenue between 9 and 8: (117 - 112) / (9 - 8) = 5 Marginal Revenue between 10 and 9: (120 - 117) / (10 - 9) = 3 Marginal Revenue between 11 and 10: (121 - 120) / (11 - 10) = 1 Marginal Revenue between 12 and 11: (120 - 121) / (12 - 11) = -1 Marginal Revenue between 13 and 12: (117 - 120) / (13 - 12) = -3

Updating the Table with Calculated Data

Now, we can fill in the calculated total revenue, marginal revenue, and average revenue data into the table: $$ \begin{array}{|c|c|c|c|c|} \hline \text { Price } & \text { Quantity } & \text { Total } & \text { Marginal } & \text { Average } \\ \hline 20 & 2 & 40 & +17 & 20 \\ \hline 19 & 3 & 57 & +15 & 19 \\ \hline 18 & 4 & 72 & +13 & 18 \\ \hline 17 & 5 & 85 & +11 & 17 \\ \hline 16 & 6 & 96 & +9 & 16 \\ \hline 15 & 7 & 105 & +7 & 15 \\ \hline 14 & 8 & 112 & +5 & 14 \\ \hline 13 & 9 & 117 & +3 & 13 \\ \hline 12 & 10 & 120 & +1 & 12 \\ \hline 11 & 11 & 121 & -1 & 11 \\ \hline 10 & 12 & 120 & -3 & 10 \\ \hline 9 & 13 & 117 & -5 & 9 \\ \hline \end{array} $$ b. As the selling price decreases, the difference between the selling price and marginal revenue also decreases. In the beginning, the difference is quite large, but as we move down the demand schedule, the marginal revenue decreases at a faster rate than the selling price, causing the gap between the two to narrow and eventually become negative.

Key concepts

Total Revenue

Total Revenue is a fundamental concept in understanding how businesses evaluate their sales performance. It represents the overall earnings a business receives from selling its goods or services. This value is calculated by multiplying the price of each unit by the number of units sold. To make this clearer, consider a simple example.
If you sell a product for $20 and manage to sell 2 units, your total revenue will be 20 multiplied by 2, which equals $40. **Why is Total Revenue Important?**

• **Measurement of Success**: Businesses use total revenue to measure how well they are doing in the market. A higher total revenue generally indicates better business performance.
• **Break-even Analysis**: It helps in determining the break-even point, where total revenues equal total costs.

Understanding your Total Revenue helps you grasp how effectively you're converting sales into income.

Marginal Revenue

Marginal Revenue is a key component of economic theory, used to understand how revenue changes with variations in sales volume. It is defined as the additional revenue that a company earns from selling one more unit of a product. Marginal Revenue is derived by finding the difference in total revenue generated by the sale of one additional unit. For instance, if the total revenue from selling 3 units is $57 and selling the fourth unit increases the total revenue to $72, the marginal revenue from that fourth unit is $15 (calculated as $72 minus $57). **Relevance of Marginal Revenue**

• **Pricing Strategy**: Helps businesses set prices to maximize profits. If Marginal Revenue falls below Marginal Cost, profits can decrease with each additional sale.
• **Market Analysis**: It provides insights into how much extra income sales will generate, which aids in decision-making processes.

Marginal Revenue acts like a compass, guiding businesses in pricing and scaling strategies.

Average Revenue

Average Revenue tells businesses how much they earn per unit on average. It is calculated by dividing the total revenue by the quantity of units sold. Simply, it's the revenue per unit. If you sold 3 units for a total revenue of $57, your average revenue per unit would be $57 divided by 3, which equals $19. **Role of Average Revenue**

• **Comparative Analysis**: Firms use average revenue to compare different time periods or segments of their business to understand performance improvement or decline.
• **Market Positioning**: Helps in assessing how a product is positioned in terms of pricing in comparison to competitors.

Average Revenue is vital for strategic pricing and can affect competition analysis.

Demand Schedule

A Demand Schedule is an essential tool for understanding consumer behavior. It describes how much of a product consumers are willing to buy at various prices. It is often represented in a table form showing different price points and the corresponding quantities desired by consumers. Take, for instance, a demand schedule where at a price of $20, 2 units are demanded, but at $19, the quantity demanded increases to 3 units. This schedule helps in visualizing the relationship between price and demand. **Importance of Demand Schedule**

• **Forecasting**: Aids in predicting how changes in prices can affect demand.
• **Production Planning**: Assists businesses in production and inventory management by predicting future sales.

This information is crucial for formulating pricing strategies and understanding market demand.

Price and Quantity Relationship

The Price and Quantity Relationship is the centerpiece of a demand curve which reflects how the quantity purchased by consumers changes with price alterations. Typically, as prices fall, the quantity demanded increases, demonstrating a negative relationship. **Key Insights from Price and Quantity Relationship**

• **Elasticity**: Measures how price changes affect the quantity demanded. A highly elastic product will see significant changes in demand with a small price change.
• **Consumer Behavior**: Helps understand consumer price sensitivity and their purchasing decisions.

The relationship between price and quantity aids in strategizing on pricing and predicting consumer reactions to price changes. Understanding this relationship provides a roadmap for optimizing sales and revenue.