One day, your father, the owner of electrical home appliance shop, obtained from a researcher the demand function for DVD players
Qd = 134 - 1.07Pv + 0.76Pc + 4.6Pm - 2.1Pd + 5M, where Qd is the quantity of DVD players, Pv is the price of a DVD, Pc is price of VCD player , Pm is the price of a movie, Pd is the price of a DVD player, and M is income and asked you to explain the meaning of this equation.
(a) What general information can you obtain from this demand function? Try to explain to your father how he should interpret this equation.
(b) Your father wants to increase the total revenue from DVD players; do you think that you can provide him any suggestions right now? What sort of additional information, if any, is required to have a valid recommendation?
(c) On another day, your father remembered that he had kept a record of the relationship between the price and sales of DVD players during the period when a “sale” with discount prices offered was conducted in late December last year. The record indicates an elastic demand for DVD players of his shop. Therefore, he recommended a permanent discount to its price to increase the sales revenue. Do you think he can achieve his objective (please give supporting rationales)?
(a) The demand function provided can provide some useful information about the relationship between the quantity of DVD players sold and various factors such as the prices of DVDs and VCD players, the price of movies, the price of DVD players themselves, and the income of consumers.
In the equation, Qd represents the quantity of DVD players sold. The rest of the variables are factors that affect the demand for DVD players:
- Pv represents the price of a DVD, indicating that as the price of DVDs increases, the demand for DVD players decreases.
- Pc represents the price of a VCD player, indicating that as the price of VCD players increases, the demand for DVD players increases.
- Pm represents the price of a movie, indicating that as the price of movies increases, the demand for DVD players increases.
- Pd represents the price of a DVD player, indicating that as the price of DVD players themselves increases, the demand for DVD players decreases.
- M represents the income of consumers, indicating that as income increases, the demand for DVD players increases.
It's important to note that the coefficients in the equation indicate the sensitivity of the quantity demanded to changes in each factor. For example, a coefficient of -1.07 for Pv means that a 1% increase in the price of DVDs will lead to a 1.07% decrease in the quantity of DVD players demanded.
(b) To provide suggestions to increase the total revenue from DVD players, additional information is required. The demand function alone cannot determine the optimal pricing strategy. Some additional information that would be helpful includes data on the current price and sales volume of DVD players, as well as information about the elasticity of demand for DVD players.
With this additional information, it would be possible to analyze the price elasticity of demand and determine the optimal pricing strategy to maximize revenue. For example, if the demand for DVD players is price elastic (meaning that a change in price has a relatively large impact on quantity demanded), lowering the price may increase the total revenue from DVD players.
(c) Given that the record of the relationship between price and sales of DVD players during the "sale" period showed an elastic demand for DVD players, it is reasonable to consider a permanent discount to increase sales revenue.
When the demand is elastic, a decrease in price results in a proportionally larger increase in quantity demanded, leading to an increase in total revenue. By offering a permanent discount on the price of DVD players, it is likely that the shop can attract more customers and sell a higher quantity of DVD players, which would ultimately increase the sales revenue.
However, it is important to consider the potential impact on profitability and costs. The shop should analyze the cost structure and pricing strategy to ensure that the permanent discount does not lead to a decrease in profitability. Additionally, monitoring customer reactions and adjusting the pricing strategy accordingly might be necessary to achieve the desired objective of increasing sales revenue.