5136 HW3 ANS
Dr. Murasko
ECON5136
ECON5136: MANAGERIAL ECONOMICS
HOMEWORK #3 ANSWERS
1. Suppose an amusement park faces demands from two consumers:
P1 = 18 – 2Q1
P2 = 14 – 2Q2
P is the price per consumer/attraction and Q is the number of consumers/attractions purchased.
Marginal cost is $2 per consumer/attraction.
a. Calculate a block pricing scheme that would approximate 1st-degree price discrimination.
Finding quantities associated with P = MC:
P1 = 18 – 2Q1 = 2
Q1 = 8
P2 = 14 – 2Q2 = 2
Q2 = 6
We now calculate the willingness-to-pay for each consumer associated with these quantities:
WTP1 = [½ (8) (18 – 2)] + ($2 x 8) = $80
WTP2 = [½ (6) (14 – 2)] + ($2 x 6) = $48
Outcome: Charge high-demand consumers $80 for 8 attractions, charge low-demand consumers
$48 for 6 attractions.
b. Does your scheme from part a satisfy incentive compatibility? Specifically, show whether high demanders would prefer the package meant for low demanders.
High-demand consumers are willing to pay a per-unit price for 6 attractions equal to:
P1 = 18 – 2(6) = $6
Their total WTP for 6 attractions is therefore:
WTP1 = [½ (6) (18 – 6)] + ($6 x 6) = $72
High-demand consumers can purchase the low-demand offer of $48 for 6 attractions and still keep $72 - $48 = $24 in consumer surplus. The first-degree strategy is not incentive compatible.
1
Dr. Murasko
ECON5136
c. Would low demanders prefer the package meant for high demanders? Explain.
Low-demand consumers are willing to pay a per-unit price for 8 attractions equal to:
P1 = 14 – 2(8) = -$2
We can see the low-demand consumers will not pay a positive per-unit price for 8 attractions.
They would not want the high-demand offer.
d. Calculate a quantity discount package that the amusement park could offer to high demanders that is also incentive compatible. Which strategy – 1st or 2nd degree – results in higher profit to the firm? What explains the difference?
The amusement park can reduce the price on the high-demand offer by $1 more than the amount
of
ECON5136
ECON5136: MANAGERIAL ECONOMICS
HOMEWORK #3 ANSWERS
1. Suppose an amusement park faces demands from two consumers:
P1 = 18 – 2Q1
P2 = 14 – 2Q2
P is the price per consumer/attraction and Q is the number of consumers/attractions purchased.
Marginal cost is $2 per consumer/attraction.
a. Calculate a block pricing scheme that would approximate 1st-degree price discrimination.
Finding quantities associated with P = MC:
P1 = 18 – 2Q1 = 2
Q1 = 8
P2 = 14 – 2Q2 = 2
Q2 = 6
We now calculate the willingness-to-pay for each consumer associated with these quantities:
WTP1 = [½ (8) (18 – 2)] + ($2 x 8) = $80
WTP2 = [½ (6) (14 – 2)] + ($2 x 6) = $48
Outcome: Charge high-demand consumers $80 for 8 attractions, charge low-demand consumers
$48 for 6 attractions.
b. Does your scheme from part a satisfy incentive compatibility? Specifically, show whether high demanders would prefer the package meant for low demanders.
High-demand consumers are willing to pay a per-unit price for 6 attractions equal to:
P1 = 18 – 2(6) = $6
Their total WTP for 6 attractions is therefore:
WTP1 = [½ (6) (18 – 6)] + ($6 x 6) = $72
High-demand consumers can purchase the low-demand offer of $48 for 6 attractions and still keep $72 - $48 = $24 in consumer surplus. The first-degree strategy is not incentive compatible.
1
Dr. Murasko
ECON5136
c. Would low demanders prefer the package meant for high demanders? Explain.
Low-demand consumers are willing to pay a per-unit price for 8 attractions equal to:
P1 = 14 – 2(8) = -$2
We can see the low-demand consumers will not pay a positive per-unit price for 8 attractions.
They would not want the high-demand offer.
d. Calculate a quantity discount package that the amusement park could offer to high demanders that is also incentive compatible. Which strategy – 1st or 2nd degree – results in higher profit to the firm? What explains the difference?
The amusement park can reduce the price on the high-demand offer by $1 more than the amount
of