Lesson 8 Assignment

Answer question 5 in “Problems and Applications” from the end of chapter 7 (p. 156). You will want to answer questions 3 and 4 first, but you are not being asked here to submit detailed answers to those questions.

Question 5. Consider a market in which Bert from problem 3 is the buyer and Ernie from problem 4 is the seller.

a.Use Ernie’s supply schedule and Bert’s demand schedule to find the quantity supplied and quantity demanded at prices of $2, $4, and $6. Which of these prices brings supply and demand into equilibrium?

b.What are consumer surplus, producer surplus, and total surplus in this equilibrium?

c.If Ernie produced and Bert consumed one less bottle of water, what would happen to total surplus?

d. If Ernie produced and Bert consumed one additional bottle of water, what would happen to total surplus?

For part (a), please fill in the chart below with appropriate numbers.

Price Quantity

Demanded Quantity

Supplied

$2 $4 $6 For parts (b)–(d), please show your calculations.

3. It is a hot day, and Bert is very thirsty. Here is the value

he places on a bottle of water:

Value of first bottle $7

Value of second bottle 5

Value of third bottle 3

Value of fourth bottle 1

a. From this information, derive Bert’s demand

schedule. Graph his demand curve for bottled

water.

b. If the price of a bottle of water is $4, how many

bottles does Bert buy? How much consumer

surplus does Bert get from his purchases? Show

Bert’s consumer surplus in your graph.

c. If the price falls to $2, how does quantity demanded

change? How does Bert’s consumer surplus

change? Show these changes in your graph.

Answer:

a)

b) At the price of $4, Bert buys two bottles of water. The value of first bottle is $7 but pays only $4 for it, therefore consumer surplus = $7 – $4 = $3. Area A in the graph is consumer surplus. The value of second bottle is $5 but pays only $4 for it with a consumer surplus = $5 – $4 = $1. Hence, Bert’s total consumer surplus = $3 + $1 = $4, which is the area of A in the figure.

c) When the price of bottle falls from $4 to $2, Bert buys three bottles. The consumer surplus includes both area A and area B. Hence, the consumer surplus rises by $7 – $2 = $5.

4. Ernie owns a water pump. Because pumping large

amounts of water is harder than pumping small

amounts, the cost of producing a bottle of water rises as

he pumps more. Here is the cost he incurs to produce

each bottle of water:

Cost of first bottle $1

Cost of second bottle 3

Cost of third bottle 5

Cost of fourth bottle 7

a. From this information, derive Ernie’s supply

schedule. Graph his supply curve for bottled water.

b. If the price of a bottle of water is $4, how many

bottles does Ernie produce and sell? How much

producer surplus does Ernie get from these sales?

Show Ernie’s producer surplus in your graph.

c. If the price rises to $6, how does quantity supplied

change? How does Ernie’s producer surplus

change? Show these changes in your graph.

Answer:

When the price of bottle is $4, Ernie sells two bottles of water. The producer surplus is area A in the figure. He received $4 for the first bottle but the cost is only $1. Hence Ernie has producer surplus of $4 – $1 = $3. He receives $4 for the second bottle which costs $3 and hence the producer surplus = $4 – $3 = $2. Therefore, the total producer surplus = $3 + $1 = $4.

When the price of bottle increases from $4 to $6, Ernie sells three bottles of water. The producer surplus consists of area A and area B.

Producer surplus from 1st bottle = $6 – $1 = $5

Producer surplus from 2nd bottle = $6 – $3 = $3

Producer surplus from 3rd bottle = $6 – $5 = $1

Total producer surplus = $5 + $3 + $1 = $9

Hence, the producer surplus increases by $5.

5. Consider a market in which Bert from Problem 3 is the

buyer and Ernie from Problem 4 is the seller.

a. Use Ernie’s supply schedule and Bert’s demand

schedule to find the quantity supplied and quantity

demanded at prices of $2, $4, and $6. Which of

these prices brings supply and demand into

equilibrium?

b. What are consumer surplus, producer surplus, and

total surplus in this equilibrium?

c. If Ernie produced and Bert consumed one less

bottle of water, what would happen to total

surplus?

d. If Ernie produced and Bert consumed one

additional bottle of water, what would happen to

total surplus?

Answer:

a)

Price Quantity supplied Quantity demanded

$2 1 3

$4 2 2

$6 3 1

b) At price $4, consumer surplus = $4 and producer surplus = $4. Hence, total surplus = $4 + $4 = $8.

c) If Ernie produces one less bottle, the producer surplus would fall to $3 (from problem 4). If Bert produces one less bottle, the consumer surplus would fall to $ (from problem 3). Hence total surplus would fall to $3 + $3 = $6.

d) If Ernie produces one additional bottle, the producer surplus would fall by $5 – $4 = $1. If Bert produces one additional bottle, the consumer surplus would fall to $4 – $3 = $1. Hence, total surplus would fall to $1 + $1 = $2.