Question

4. As the manager of a local hotel chain, you have hired an econometrician to estimate the demand for one of your hotels (H). The estimation has resulted in the following demand function:

QH = 3,000 – PH – 1.8PC – 2.5PSE + 2.4POH + .01M, where,

PH is the price of a room at your hotel, PC is the price of concerts in your area,

PSE is the price of sporting events in your area,

POH is the average room price at other hotels in your area, M is the average income in the United States.

What would be the impact on your firm of each following scenarios?

(all answers should indicate the precise increase or decrease in the number of rooms rented)

1. A $4,000 increase in income?
2. A $30 reduction in the price charged by other hotels?
3. A $40 increase in the price of tickets to local sporting events?
4. A $25 increase in the price of concert tickets, accompanied by a $500 decrease in income?

Answer 1

QH = 3,000 – PH – 1.8PC – 2.5PSE + 2.4POH + 0.01M

(a)

Coefficient of M is 0.01, meaning that if income increases by $1, demand will increase by 0.01 units.

When income increases by $4,000, demand will increase by ($4,000 x 0.01) = 40.

(b)

Coefficient of POH is 2.4, meaning that if price charged by other hotels decreases by $1, demand will decrease by 2.4 units.

When price charged by other hotels decreases by $30, demand will decrease by ($30 x 2.4) = 72.

(c)

Coefficient of PSE is -2.5, meaning that if price of sports events increases by $1, demand will decrease by 2.5 units.

When price of sports events increases by $40, demand will decrease by ($40 x 2.5) = 100.

(d)

(i) Coefficient of PC is -1.8, meaning that if price of concerts increases by $1, demand will decrease by 1.8 units.

When price of concerts increases by $25, demand will decrease by ($25 x 1.8) = 45.

(ii) When income decreases by $500, demand will decrease by ($500 x 0.01) = 5.

(iii) Therefore, net decrease in demand = 45 + 5 = 50