Question

Show all your work

1. Consider that you are the newly appointed marketing manager of a factory that manufactures cashmere socks. To help you devise new marketing strategies, you decided to conduct market demand analysis for your product. To that end, you decided to estimate the market demand function for your product and the estimated market demand for your output is as follows.  

Q = 1000 - 400PS + 1.5PW + 0.5M + 1.2A

Where:

Q = Annual quantity demanded of pairs of cashmere socks

PS = Price of one pair of cashmere socks

PW = Price of one pair of wool socks

M = average income in dollar of customers per year

A = number of ads per year.

Suppose at the present Ps = $10, Pw = $5, M = $20,000, and A = 300 units.

a. What is the price elasticity of demand of your product?

b. What is the cross-price elasticity of demand of your product with respect to the price of the related product, wool socks?

c. What is the income elasticity of demand of your product?

d. A recent report in The Wall Street Journal says that national income is expected to rise by 2 percent this year. Using the information in part c, what do you expect will happen to number pairs you will be able to sell?

Answer 1

Q = 1000 - 400PS + 1.5PW + 0.5M + 1.2A

Plugging in given values,

Q = 1,000 - (400 x 10) + (1.5 x 5) + (0.5 x 20,000) + (1.2 x 300)

Q = 1,000 - 4,000 + 7.5 + 10,000 + 360

Q = 7,367.5

(a) Price elasticity of demand = (dQ/dPs) x (Ps/Q) = - 400 x (10/7,367.5) = - 0.54

(b) Cross elasticity of demand = (dQ/dPw) x (Pw/Q) = 1.5 x (5/7,367.5) = 0.001

(c) Income elasticity of demand = (dQ/dM) x (M/Q) = 0.5 x (20,000/7,367.5) = 1.36

(d) Income elasticity = % Change in demand / % Change in income

1.36 = % Change in demand / 2%

% Change in demand = 1.36 x 2% = 2.72%

So my sales will increase by 2.72%.

New sales = 7,367.5 x 1.0272 = 7,567.90