Question

In: Economics

Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup...

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: $

Solutions

Expert Solution

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


Related Solutions

Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup...
Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup of lemonade costs Beth $0.20 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 $0.50 $0.45 $0.40 $0.35 $0.30 $0.25 $0.20 $0.15 $0.10 $0.05 Beth knows the distribution of reservation prices (that...
Kent sells lemonade in a competitive market on a busy street corner. His production function is...
Kent sells lemonade in a competitive market on a busy street corner. His production function is F(L, K) = L1/3 K1/3 where output q is gallons of lemonade, K is the pounds of lemons he uses and L is the number of labour-hours spent squeezing them. The corresponding marginal products are MPL= 13L-23K13 and MPK= 13L13K-23. Every pound of lemons cost r and the wage rate of lemon squeezers is w. Prove that this production process has decreasing returns to...
Earnie sells lemonade at a busy street corner in Rollaville. His production function is f(x,y) =...
Earnie sells lemonade at a busy street corner in Rollaville. His production function is f(x,y) = x^1/4*y^1/2 where output is measured in gallons, x is the number of pounds of lemons he uses, and y is the number of labor-hours spent squeezing them. The price of a pound of lemons is $1 and the wage rate for the lemon-squeezer (Earnie’s best friend, Bert) is also $1. While Earnie can hire Bert for any amount of time, he has only three...
Kelly sells orange juice in a competitive market on a busy street corner in New York....
Kelly sells orange juice in a competitive market on a busy street corner in New York. Her production function is ?(?1, ?2) = ?1 1/3 ?2 1/3, where output is measured in gallons, ?1 is number of pounds of oranges she uses, and ?2 is the number of labor-hours spent squeezing them. ?1 = $16 is the cost of a pound of oranges and ?2 = $2 is the wage rate for orange-squeezers. At the cost minimizing input bundle, how...
Who is your favorite character in Fahrenheit 451? Explain your answer. Who is your second-favorite character...
Who is your favorite character in Fahrenheit 451? Explain your answer. Who is your second-favorite character in the novel? Explain your answer.
Hanna, who is a 5-year-old girl, eats nothing but pasta, yogurt, and lemonade. Each month her...
Hanna, who is a 5-year-old girl, eats nothing but pasta, yogurt, and lemonade. Each month her parents buy 25 pounds of pasta, 65 packages of yogurt, and 15 bottles of lemonade. These three items make up a basket of goods and services similar to the much larger basket used by the Bureau of Labor Statistics (BLS) when computing the official Consumer Price Index (CPI). The table below lists the average price for each item in this basket for the past...
Four teenagers live on your street. Each is willing to shovel snow from one driveway each...
Four teenagers live on your street. Each is willing to shovel snow from one driveway each day. Their “willingness to shovel” valuations (supply) are: Jean, $10; Kevin, $9; Liam, $7; Margaret, $5. Several households are interested in having their driveways shoveled, and their willingness to pay values (demand) are: Jones, $8; Kirpinsky, $4; Lafleur, $7.50; Murray, $6. (a) Draw the implied supply and demand curves as step functions. (b) How many driveways will be shoveled in equilibrium? (c) Compute the...
21-B Book Street Books sells about 13701370 books each month. The circle graph displays the most...
21-B Book Street Books sells about 13701370 books each month. The circle graph displays the most popular book categories, by percentage, each month. Categories of Books Sold nonfiction 20.4%20.4% computer 43% science fiction 10% sports 11% mystery 15.6% Step 1 of 5: Find the number of nonfiction books sold each month. Round your answer to the nearest integer. Step 2 of 5: Find the number of computer books sold each month. Round your answer to the nearest integer. Step 3...
Your next project will take place on a two-lane street (each lane is 12 ft wide)....
Your next project will take place on a two-lane street (each lane is 12 ft wide). The posted speed limit is 45 mph. You will have to close one lane of this street. Write the components/elements of the Temporary Traffic Control (TTC) that you will utilize. Include the minimum required dimension of all components of your plan.
A firm sells to consumers who each have a demand demand function given by QD =...
A firm sells to consumers who each have a demand demand function given by QD = 80 - P. It has constant marginal cost C = 20 with no fixed cost. Compared to the optimal two-part tariff, a policy of "buy the first 20 units for $60 each and get the next 20 for $40 each" would yield: A. $600 less in profits B.$400 less in profits C.$200 less in profits D. The same profits because the average price is...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT