# Calculate the marginal revenue of selling an additional cup of lemonade

- Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup of lemonade costs Beth 20 cents to produce; she has no fixed costs. The reservation prices for the 10 people who walk by Beth’s lemonade stand each hour are listed in the table below. Beth knows the distribution of reservation prices (that is, she knows one person is willing to pay $1.00, another $0.90, and so on), but does not know any specific individual’s reservation price.
- Calculate the marginal revenue of selling an additional cup of lemonade. (Start by figuring outthe price Beth would charge if she produced only one cup of lemonade, and calculate the total revenue; then find the price she would charge if she sold two cups of lemonade; and so on.)

Person |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |

Reservation price |
$1.00 |
$0.90 |
$0.80 |
$0.70 |
$0.60 |
$0.50 |
$0.40 |
$0.30 |
$0.20 |
$0.10 |

Quantity in cups |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |

Total revenue |
$1.00 |
$1.80 |
$2.40 |
$2.80 |
$3.00 |
$3.00 |
$2.80 |
$2.40 |
$1.80 |
$1.00 |

Marginal revenue |
$1.00 |
$0.80 |
$0.60 |
$0.40 |
$0.20 |
$0 |
-$0.20 |
-$0.40 |
-$0.60 |
-$0.80 |

- What is Beth’s profit maximizing price and quantity?
*Answer*: MR = MC at a price of $0.60 and quantity of 5 cups. - At that price, what are Beth’s economic profit and total consumer surplus?

*Answer*: Profit = (P - MC) Q = (0.60 - 0.20) 5 = $2. Consumer surplus is reservation price minus actual price for each cup sold: ($1.00 - $0.60) + ($0.90 - $0.60) + ($0.80 - $0.60) + ($0.70 $0.60) = $1.

- What price should Beth charge if she wants to maximize total economic surplus? Whatquantity would she sell? How much would total economic surplus be?

*Answer*: She should set P = MC = $0.20. Nine (or eight) cups of lemonade would be sold. Total economic surplus is reservation price minus marginal cost for each cup sold: ($1.00 - $0.20) + ($0.90 - $0.20) + ($0.80 - $0.20) + ($0.70 - $0.20) + ($0.60 - $0.20) + ($0.50 - $0.20) + ($0.40 $0.20) + ($0.30 - $0.20) = $3.60.

- Now suppose Beth can tell the reservation price of each person. What price would she chargeeach person if she wanted to maximize profit? Compare her profit to the total surplus calculated in part d.

*Answer*: She would charge persons A through I (but not J) their respective reservation prices.

Doing so would earn a profit of $3.60, which is the same as the total economic surplus in part d.

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