Question

Problem 2. A college is able to admit a student for $5 (so that MC=AC=5 and FC=0). There are 9 applicants whose willingness to pay are $26, $23, $20, $17, $14, $11, $8, $5, and $2. a) Fill in the college’s demand schedule. Compute the Total Revenue and the Marginal Revenue. Quantity 1 2 3 4 5 6 7 8 9 Price 26 23 20 17 14 11 8 5 2 TR MR b) Fill in the table using the information below. Price Quantity Profit CS DWL TS Efficient Outcome P=MC=$5 Monopoly (Single price) Group Pricing Perfect PD Efficient Outcome: The college admits applicants at marginal cost. Single Price: The college is acting as a profit-maximizing monopolist. Group Pricing: Assume that the applicants with willingness to pay $26, $23, $20, $5, and $2 are out of state, while the applicants with willingness to pay $17, $14, $11, and $8 are in state. The college can charge one price for in-state applicants, and a different price for out-of-state applicants. Perfect Price Discrimination: The college charges every applicant according to their willingness to pay. c) For group pricing, use the following table: Out of State In State Quantity 1 2 3 4 5 Quantity 1 2 3 4 Price Price TR TR MR MR d) Compare the single price and the group pricing outcome in terms of prices, quantities, and consumer surplus. Price Quantity CS

Answer 1

a. The college's demand schedule is 9, 8, 7, 6, 5, 4, 3, 2, 1. The total revenue is $147. The marginal revenue is $5 for the first 5 seats, then $4, $3, $2, $1, and $0.

b. The efficient outcome is the most efficient, followed by group pricing, then the single price, and then perfect price discrimination.

c. The out-of-state price is $20. The in-state price is $8. The out-of-state quantity is 3. The in-state quantity is 5. The total revenue is $104. The marginal revenue is $8.

d. The single-price outcome has a price of $17 and a quantity of 5. The group-pricing outcome has a price of $20 (out-of-state) and $8 (in-state) and a quantity of 7. The single-price outcome has a consumer surplus of $54, while the group-pricing outcome has a consumer surplus of $84.

a)

The college's demand schedule shows the number of students it is willing to admit at each price. The total revenue is the total amount of money the college makes from selling seats to students. The marginal revenue is the additional revenue the college makes from selling one more seat.

b) Fill in the table using the information below.

The table shows the price, quantity, profit, consumer surplus, deadweight loss, and total surplus for each of the four pricing outcomes: efficient outcome, monopoly, group pricing, and perfect price discrimination.

Outcome Price Quantity Profit CS DWL TS

Efficient Outcome $5 9 $0 $126 $0 $126

Monopoly $17 5 $60 $54 $33 $87

Group Pricing $20 (out-of-state), $8 (in-state) 7 (3 out-of-state, 4 in-state) $70 $84 $14 $98

Perfect Price Discrimination $26, $23, $20, $17, $14, $11, $8, $5, $2 9 $126 $0 $0 $126

c) For group pricing, use the following table:

The table shows the price, quantity, total revenue, and marginal revenue for each quantity of out-of-state and in-state students.

| Out-of-State | Quantity | Price | TR | MR | In-State | Quantity | Price | TR | MR |

| | 1 | $26 | $26 | − | | 1 | $8 | $8 | − |

| | 2 | $26 | $52 | − | | 2 | $8 | $16 | − |

| | 3 | $20 | $60 | $8 | | 3 | $8 | $24 | $8 |

| | 4 | $20 | $80 | $0 | | 4 | $8 | $32 | $0 |

d)

The single-price outcome has a higher price and lower quantity than the group-pricing outcome. The single-price outcome also has lower consumer surplus than the group-pricing outcome.