Exercise 1
The marketing manager has estimated the company’s demand curve with the equation P=3000 – 40Q. To develop a deeper understanding of pricing and quantity to be produced, complete the following analyses:
1. Draw the demand curve (use a range of Q values from 20 to 60).
2. Calculate revenue variation with quantity and determine the price that maximizes revenue.
3. Calculate price elasticity of demand. At what quantity the demand is unit-elastic? Identify the elastic and inelastic range for demand.
4. What price and quantity would you recommend to your CEO?
Exercise 2
Your company is considering a price reduction on a product which currently sells for the price of $5.00. You know the price elasticity for the product is roughly equal to -2.3 over the range being considered for the price change. The product has been selling at the brisk pace of 500 per week. To increase market share, you would like to increase sales to 750 per week. What price should you set?
Exercise 3
We know that the demand curve always slopes downward. Your friend shows you a demand diagram for “prestige goods” that has an upward demand curve. He argues that for prestige goods the higher the price, the greater the demand for the product. You know the demand curve cannot slope upward. How can you explain the diagram your friend is showing you for prestige goods?
Exercise 1:
1. To draw the demand curve, we need to plot the price (P) on the vertical axis and the quantity (Q) on the horizontal axis. The demand curve equation is given as P = 3000 - 40Q. We can select a range of Q values from 20 to 60 and calculate the corresponding P values using the equation. For example, when Q = 20, P = 3000 - 40(20) = 2200. Similarly, we can calculate P for other Q values within the range. Plotting these points on a graph and connecting them will give us the demand curve.
2. Revenue (R) is calculated as the product of price (P) and quantity (Q), i.e., R = P * Q. To determine the price that maximizes revenue, we need to find the value of P that results in the highest R. One way to do this is to calculate the revenue for different price levels and compare them. For example, we can calculate revenue for P = 3000 - 40Q when Q = 20, 30, 40, ..., 60. The price that yields the highest revenue will be the one that maximizes revenue.
3. Price elasticity of demand (PED) measures the responsiveness of quantity demanded to changes in price. PED is calculated as the percentage change in quantity divided by the percentage change in price. To calculate PED at a specific quantity, we need to calculate the percentage change in quantity and price when there is a small change in price. If PED is equal to 1, the demand is unit-elastic. To identify the elastic and inelastic range for demand, we can calculate PED for different quantities within the given range and determine whether it is greater or less than 1.
4. To recommend a price and quantity to the CEO, we need to consider multiple factors such as the company's cost structure, competition, market conditions, and the desired profit margin. Analyzing the demand curve and revenue variation can provide insights into pricing and quantity decisions, but additional factors need to be taken into account to make a comprehensive recommendation.
Exercise 2:
To determine the price that will increase sales to 750 per week, we can use the price elasticity (PED) formula:
PED = (Percentage change in quantity demanded) / (Percentage change in price)
Given that PED is -2.3, and the current sales are 500 per week, we can calculate the percentage change in quantity demanded:
Percentage change in quantity demanded = (750 - 500) / 500 = 0.5
To find the desired price, we can rearrange the PED formula:
-2.3 = 0.5 / (Percentage change in price)
Solving for the percentage change in price:
(Percentage change in price) = 0.5 / (-2.3) = -0.2174
We can then calculate the new price as a percentage of the current price:
New price = $5.00 - (0.2174 * $5.00) = $5.00 - $1.09 = $3.91
Therefore, to increase sales to 750 per week, the price should be set at $3.91.
Exercise 3:
If your friend is showing you an upward-sloping demand curve for prestige goods, it contradicts the basic concept of demand. Generally, demand curves slope downward because as the price increases, the quantity demanded decreases. This is based on the law of demand.
However, prestige goods are unique in that they carry a certain level of exclusivity or status symbol value. In some cases, for luxury or prestige goods, there may be a segment of consumers who perceive higher prices as an indicator of quality or status. This means that for these specific goods, the higher the price, the greater the demand among this niche group of consumers seeking exclusivity.
Thus, the demand curve for prestige goods may exhibit an upward slope in the context of this specific segment of consumers. However, it is important to note that this is not a general characteristic of demand curves and does not apply to most goods and services.