Question

Suppose that the demand (sales) function for a product A has been estimated as:

? =10.5−.8? −.2? +.1? +.0005? ? ???

Where, ?? is the quantity of product A demanded, in thousand per month.

? is the price of product A;

? is the price of product B, which is currently $10; ?

? is the price of product C, which is currently $5; and ?

Y is the level of per capita income, which is currently $10,000.

1. Of the following changes, which one would cause an increase in the demand for product A: a decrease in the price of product A, an increase in the price of product A, an increase in the price of product B, an increase in the price of product C, or a decrease in the level of per capita income.

2. Is product A normal or inferior? Are product A and product B substitutes or complements? Are product A and product C substitutes or complements?

3. Express the relationship between expected sales of product A and the price of product A alone.

4. When the price of product A is $5, what is the amount of expected sales of product A?

5. If a demand curve were graphed for product A, what would be the equation for graphical

demand

Answer 1

Q_A=10.5-0.8P_a-0.2P_b+0.1P_c+0.005Y................(1)

Q_A= Quantity of Product A demanded,in thousand per month

Pa=Price of product A

Pb=Price of product B which is currently $10

Pc=Price of product C which is currently $5

Y=Per capita income which is currently $10,000

The Coefficient of Pa represents that Cetris paribus,a $1 rise in the price of a results in decline in the demand of A by 8000 units per month

The Coefficient of Pb represents that Cetris paribus a $1 rise in the price of b results in decline in the demand of A by 2000 units per month

The Coefficient of Pc represents that Cetris paribus a $1 rise in the price of c results in rise in the demand of A by 1000 units per month

The Coefficient of Y represents that Cetris paribus a $1 rise in Y results in rise in the demand of A by 5 units per month

There would be an increase in the demand for product A if there is decrease in the price of product A ,decrease in the price of product B and rise in the price of product C and an increase in per capita income.

1 There would be rise in the demand of product A if there is decrease in the price of product A and an increase in the price of product C

2 A is a normal good due to positive sign of the coefficient of Y(A good is defined to be normal if its demand increases with the rise in per capita income)

Product A and Product B are complements (Since rise in the price of product B results in the fall in the quantity demanded of A.(For Example when price of milk rises then quantity demanded of tea falls )

Product A and Product C are substitutes(Since rise in the price of product C results in rise in the quantity demanded of product A .For Example,when price of Coca cola rises then quantity demanded of Pepsi decreases)

3 Cetreris paribus,there is an inverse relationship between the price of A and expected sales of A

4 Expected Sales of A at price A=5

Pb=Price of product B which is currently $10

Pc=Price of product C which is currently $5

Y=Per capita income which is currently $10,000

By putting these values in equation (1)

Expected Sales of A=10.5-0.8P_a-0.2P_b+0.1P_c+0.005Y.

                             =10.5-0.8*5-0.2*10+0.1*5+0.005*10,000

                              = 55,000 per month

5 QA=59 -0.8Pa (As the demand curve equation shows relationship between Pa and Qa assuming other factors remaining constant )