The market demand for Brand x has been estimated as: Qxd=1500-3px-005M-25Py+75Pz

where Px is the price of Brand x, M per capita income, Py is the price of Brand y, and Pz is the price of Brand z.

Note: Given coefficient of Px, coefficient of Py and Pz should be -2.5 and 7.5 respectively and not coefficient of Py and Pz -25 and 75 respectively as given above.

Also coefficient of M to 0.05.

 

a) With respect to changes in per capita income, what kind of good is Brand x?

Sol: Since coefficient of M (per capita income) is negative in demand function, with increase in income, demand for Brand X decreases so Brand x is inferior good. As inferior goods are those whose demand drops when one's incomes increases.

b) How are Brands x and y related?

Sol: As the coefficient of Py is negative, Brands Y is a compliments for Brands X. Therefore, whenever Py changes, Qxd will change in the opposite direction. This is what happens when the two goods are compliments for each other.

The coefficient of Py is negative means an increase in the price of Brands Y (Py) will cause consumer to purchase less of Brands X causing Qxd to decrease.

c) How are Brands x and z related?

Sol: As the coefficient of Pz is a positive number, Brands Z is a substitute for Brands X. Therefore, whenever Pz changes, Qxd will change in the same direction. This is what happens when the two goods are substitutes for each other.

The coefficient of Pz is positive means an increase in the price of Brands z (Pz) will cause consumer to purchase more of Brands X causing Qxd to increase.

d) How are Brands z and y related?

Sol: As the coefficient of Py is negative and the coefficient of Pz is a positive, this implies Brands z and y are complimentary goods as the coefficients are of opposite sign.

Complementary goods are products which are used together. They cannot be used without each other are known to have a strong relationship. In other words, when the price goes up on one, the demand goes down for the other good.

e) What is the market demand for Brand x?

Sol: The market demand for Brand x has been estimated as: Qxd=1500-3px-0.05M-2.5Py+7.5Pz

where Px is the price of Brand x, M per capita income, Py is the price of Brand y, and Pz is the price of Brand z.

Also given that that Px=$2 , M=$20,000 , Py=$4 , and Pz=$4.

The market demand for Brand x : Qxd = 1500 – 3*2 – 0.05*20,000 – 2.5*4 + 7.5*4 = 514

Hence, the market demand for Brand x is 514.