Question

1. Define the elements of the following equation: P = a0 ‒ a1 × Qd.

2. Given P = $150 ‒ 0.005 × Qd as the demand for a professional sports team:

a. If P = $60, what is Qd?

b. If P = $40, what is Qd?

3. Imagine these two possible changes from the demand curve listed in Question 2: a. P = $175 ‒ 0.005 × Qd b. P = $125 ‒ 0.005 × Qd

For each, identify whether Question 3(a) or 3(b) would be consistent with the following stated changes:

iii.increase in the size of the market where the team plays

iv.decrease in the per-capita income in the market where the team plays

v.move to a newer stadium

vi.decline in the quality of players employed by the team

Answer 1

1. P = a0 ‒ a1 × Qd
a0 is the vertical intercept which states the value of price when Qd is zero and -a1 is the slope which states the slope of the demand function, that is, change in price to change in quantity demanded. Negative value indicates that demand curve is downward sloping. So, this equation shows the relationship between P and Qd where P is the price and Qd is the quantity demanded.

2. P = $150 ‒ 0.005 × Qd
a. P = $60 = 150 ‒ 0.005 × Qd
So, 0.005 × Qd = 150 - 60 = 90
So, Qd = 90/0.005 = 18,000
Qd = 18,000

b. P = $40 = 150 ‒ 0.005 × Qd
So, 0.005 × Qd = 150 - 40 = 110
So, Qd = 110/0.005 = 22,000
Qd = 22,000

3. a. P = $175 ‒ 0.005 × Qd b. P = $125 ‒ 0.005 × Qd
3(a) shows increase in demand and 3(b) shows decrease in demand.

iii. increase in the size of the market where the team plays increases the demand for sports team so it is consistent with 3(a).
iv. decrease in the per-capita income in the market where the team plays decreases the demand for sports team so it is consistent with 3(b).
v. move to a newer stadium increases the demand for sports team so it is consistent with 3(a).
vi. decline in the quality of players employed by the team decreases the demand for sports team so it is consistent with 3(b).