Question

Vincent operates a scenic tour business in Boston. He has one bus which can fit 50 people per tour and each tour lasts 2 hours. His total cost of operating one tour is fixed at $450. Vincent’s cost is not reduced if he runs a tour with a partially full bus. While his cost is the same for all tours, Vincent charges each passenger his/her willingness to  pay: adults $18 per trip, children $10 per trip, and senior citizens $12 per trip. At those rates, on a typical day Vincent’s demand is:

Passenger Type	Willingness to Pay	Demand per day
Adults	$18	70
Children	$10	25
Senior Citizens	$12	55

Assume that Vincent’s customers are always available for the tour; therefore, he can fill his bus for each tour as long as there is sufficient total demand for the day.

1-Vincent uses a pricing practice called?

2- What is Vincent’s cost of serving all passengers demanding a tour on a typical day?

3-What is Vincent’s profit on a typical day?

4-One of Vincent’s friends tells him he would be more profitable if he charged a single price of $18. Assuming no changes in consumer demand, what would Vincent’s profit be if he charged everycustomer $18?

5- One of Vincent’s friends tells him he would be more profitable if he charged a single price of $12. Assuming no changes in consumer demand, what would Vincent’s profit be if he charged every customer $12?

Answer 1

1) Vincent uses a pricing practice called first degree price discrimination. When a firm charges a different price from each customer equal to willingness to pay of each respective customer then such pricing behavior is referred to as first degree price discrimination.

2) No. of tour operates by Vincent on a typical day = Adult Demand + Children demand + Senior Citizens Demand / Bus Capacity

= 70 + 25 + 55 / 50

= 150 / 50

= 3.

Total cost per tour is $450.

Thus, total cost for 3 hours on a typical day = $450 * 3 = $1350.

3) Total revenue on a typical day:
= (Adult Demand * Willingness to pay) + (Children demand * Willingness to pay) + (Senior Citizens Demand * Willingness to pay)

= (70*$18) + (25*$10) + (55*$12)

= $1260+$250+$660

= $2170.

Thus, Profit = Total revenue - Total cost

= $2170 - $1350

= $820.

4) Now, if he charged a single price of $18:

Total revenue on a typical day:
= (Adult Demand * $18) + (Children demand * $18) + (Senior Citizens Demand * $18)

= (70*$18) + (25*$18) + (55*$18)

= $1260+$450+$990

= $2700.

Thus, Profit = Total revenue - Total cost

= $2700 - $1350

= $1350.

Thus, if Vincent charges a price of $18, then his profit is $1350, which is greater than the previous profit of $820.

5) Now, if he charged a single price of $12:

Total revenue on a typical day:
= (Adult Demand * $12) + (Children demand * $12) + (Senior Citizens Demand * $12)

= (70*$12) + (25*$12) + (55*$12)

= $840+$300+$660

= $1800.

Thus, Profit = Total revenue - Total cost

= $1800 - $1350

= $450.

Thus, if Vincent charges a price of $18, then his profit is $450, which is less than the previous profit of $1350.