Wilpen Company, a price-setting firm, produces nearly 80 percent of all tennis balls purchased in the United States. Wilpen estimates the U.S. demand for its tennis balls by using the following linear specification;
Q = a + bP + cM + dPr
Where Q is the number of can of tennis balls sold quarterly, P is the wholesale price Wilpen charges for a can of tennis balls, M is the consumer’s average household income
do you have a question?
To answer your question, we need to find out how changes in price (P) and consumer's average household income (M) affect the demand for tennis balls (Q).
The equation provided, Q = a + bP + cM + dPr, is a linear specification used to estimate the demand for tennis balls. Let's break down the variables:
- Q: The number of cans of tennis balls sold quarterly. This is the dependent variable or the variable we want to explain.
- a, b, c, and d: These are the coefficients or parameters that need to be estimated. They determine the impact of price and income on the demand for tennis balls. We'll need more information or data to calculate these coefficients.
- P: The wholesale price that Wilpen charges for a can of tennis balls. This is one of the independent variables that affect the demand for tennis balls. When the price increases, the quantity demanded usually decreases, and vice versa.
- M: The consumer's average household income. This is another independent variable that influences the demand for tennis balls. As income rises, people tend to purchase more tennis balls, and as income falls, they may buy fewer tennis balls.
- Pr: The price of a related good, such as a substitute for tennis balls. This variable accounts for the impact of the price of substitutes on the demand for tennis balls. For example, if the price of a substitute product increases, people may switch to buying more tennis balls, increasing the quantity demanded.
To estimate the coefficients a, b, c, and d, and understand the specific impact of price and income, Wilpen Company would typically collect data on tennis ball sales (Q), wholesale prices (P), average household income (M), and the price of substitutes (Pr) over time. They would then use statistical methods such as regression analysis to estimate the coefficients.
Once the coefficients are estimated, the equation can be used to predict the demand for tennis balls based on changes in price and income. For example, if Wilpen were to raise the wholesale price (P), they could determine the corresponding decrease in quantity demanded (Q) using the estimated coefficient (b).
In summary, the given equation provides a framework for estimating the demand for tennis balls based on price (P), consumer income (M), and the price of substitutes (Pr). The coefficients in the equation need to be estimated using data to understand the specific impact of these variables on the quantity demanded (Q).