Question

Assume you are an analyst at a firm that operates a chain of department stores that specializes in women shoes. Your own research produced the following demand function for women's running shoes: Qrs = 10,000 − 10Prs − 20Ps + 1/1000M

Where grs is the quantity of running shoes demanded, Prs is the price of running shoes, Ps is the price of a single pair of socks, and M is the consumer's income. Suppose that the average price of running shoes is Prs =$100, the average price of socks is Ps=$20, and the average consumer's income is M= $100,000, (a) What is the average demand for running shoes?

Answer 1

The average demand for women's running shoes is calculated using the demand function by plugging in the values for the price of running shoes, the price of socks, and consumer's income. With the prices at $100 for running shoes, $20 for socks, and the income at $100,000, the average demand comes out to be 8,700 pairs.

Step-by-step explanation:

The student inquiry concerns the calculation of the average demand for women's running shoes based on a given demand function. To find the average demand, we can input the given average prices and consumer income into the demand function Qrs = 10,000 - 10Prs - 20Ps + 1/1000M. Given that Prs = $100 (price of running shoes), Ps = $20 (price of socks), and M = $100,000 (consumer's income), the calculation would be:

Qrs = 10,000 - 10(100) - 20(20) + 1/1000(100,000)

Qrs = 10,000 - 1000 - 400 + 100

Qrs = 8,700

Therefore, the average demand for women's running shoes, when the average price of running shoes is $100, the average price of socks is $20, and the average consumer's income is $100,000, is 8,700 pairs.