In: Economics
Beth is a second-grader who sells lemonade on a street corner in
your neighborhood. Each cup of lemonade costs Beth $0.90 to
produce; she has no fixed costs. The reservation prices for the 10
people who walk by Beth's lemonade stand each day are listed in the
following table.
Person | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Reservation price |
$1.50 | $1.40 | $1.30 | $1.20 | $1.10 | $1.00 | $0.90 | $0.80 | $0.70 | $0.60 |
Beth knows the distribution of reservation prices (that is, she
knows that one person is willing to pay $1.50, another $1.40, and
so on), but she does not know any specific individual’s reservation
price.
a. Calculate the marginal revenue of selling an additional cup of
lemonade. (Start by figuring out the price Beth would charge if she
produced only one cup of lemonade, and calculate the total revenue;
then find the price Beth would charge if she sold two cups of
lemonade; and so on.)
Instructions: If you are entering any negative
numbers be sure to include a negative sign (-) in front of those
numbers. Enter your responses rounded to two decimal
places.
Price | Quantity |
Total revenue ($ per day) |
Marginal revenue ($ per cup) |
1.50 | 1 | ||
1.40 | 2 | ||
1.30 | 3 | ||
1.20 | 4 | ||
1.10 | 5 | ||
1.00 | 6 | ||
0.90 | 7 | ||
0.80 | 8 | ||
0.70 | 9 | ||
0.60 | 10 |
b. What is Beth’s profit-maximizing price?
Instructions: Enter your response rounded to two
decimal places.
$ .
c. At that price, what are Beth’s economic profit and total
consumer surplus?
Instructions: Enter your responses rounded to two
decimal places.
Economic profit: $ per day.
Consumer surplus: $ per day.
d. What price should Beth charge if she wants to maximize total
economic surplus?
Instructions: Enter your response rounded to two
decimal places.
Price to maximize total economic surplus: $
a. Beth's Marginal revenue (MR) is in the table below (last column):
Quantity | Price | TR | MR |
1 | 1.50 | 1.50 | - |
2 | 1.40 | 2.80 | 1.30 |
3 | 1.30 | 3.90 | 1.10 |
4 | 1.20 | 4.80 | 0.90 |
5 | 1.10 | 5.50 | 0.70 |
6 | 1.00 | 6.00 | 0.50 |
7 | 0.90 | 6.30 | 0.30 |
8 | 0.80 | 6.40 | 0.10 |
9 | 0.70 | 6.30 | -0.10 |
10 | 0.60 | 6.00 | -0.30 |
b. $ 1.20
reason: Beth's profit maximizing price is where MC = MR =
0.90.
MR is 0.90 when quantity is 4. Price for this output is $1.20.
c. (i) Economic profit = $1.20
reason: Economic profit = (Price - cost) * quantity => (1.20 - 0.90) * 4 => 0.30 * 4 = 1.20
(ii) Consumer surplus = $0.60
reason: Consumer surplus is the difference between the reservation price and the actual price
There are 3 consumers whose resevation price is higher than the actual price:
Cons No Surplus Cons surplus |
(reservation - actua) |
1 1.50 - 1.20 0.30 |
2 1.40 - 1.20 0.20 |
3 1.30 - 1.20 0.10 |
Total consumer suplus = 0.60 |
d. $0.90
reason: To maximize economic surplus, she should produce
quantity where Price= MC = 0.90.
When price = 0.90, quantity = 7. So, price =
0.90