Question

There is an answer sheet for question 3 and 4 at the end for you to check.

Please show your work.

1. Consider our favorite demand curve P = 10 –Q. If the price is set at $7 what is our total consumer surplus? $5? $3?

2. For the supply curve P = 2 + .5Q, if the price is set at $7 what is our total producer surplus? $5? $3?

3. Suppose the market for watermelons can be described by the graph below.

a. If Jon is willing to pay as much as $8 for a watermelon, how much surplus would he receive if he pays the market price for a watermelon?

b. Suppose Figgy Farms requires at least $5 per watermelon to be willing to sell in this market. What is Figgy's producer surplus for one watermelon in this market?

c. How much total consumer surplus is received in this market?

d. How much total producer surplus is received in this market?

e. What is the total surplus (combined consumer and producer surplus) in the market?

4. Suppose a market for burritos is given by:

Qd = 40 – 5P

QS = -20 + 10P

a. Graph the supply and demand schedules

b. Determine the equilibrium price and quantity

c. Calculate the consumer and producer surpluses – identify on your graph

d. Assume a price floor of $6 – calculate what happens

Answers:

#3

a.​Consumer surplus is the difference between the maximum Jon is willing to pay and the price he actually pays. The equilibrium price in this market is $6, so his consumer surplus is $2. $2 = $8 – $6.

b.​Producer surplus is the difference between the market price and the minimum a seller requires to offer the product for sale. In this case, Figgy's producer surplus is $6 – $5 = $1.

c.​Total consumer surplus is the area below the demand curve but above the market price. The area of this triangle on the graph is ½ x ($11 – $6) x 200 = $500.

d.​Total producer surplus is the area above the supply curve but below the market price. The area of this triangle on the graph is ½ x ($6 – $4) x 200 = $200.

e.​The total surplus is the sum of consumer and producer surplus, or $500 + $200 = $700.

#4.

b. 40 – 5p = -20 +10P

60 = 15P

P=4, Q = 20

c. CS = 4x20x.5 = 40

PS = 2x20x.5 = 20

d. 15 DWL

Answer 1

I suppose you are looking for answers of question 1 and 2 since you already have solutions for question 3 and 4. If I'm wrong let me know through comment section.

1. The demand curve is given as,

P = 10 - Q.

And price is given as P = $7.

Quantity demanded at this price will be equal to,

Q = 10 - P

Q = 10 - 7

Q = 3

The formula to calculate the consumer surplus is,

= 1/2 × (maximum willingness to pay - price) × Q

The maximum willingness to pay is calculated by Putting Q = 0 in demand function. So putting Q = 0, we get

P = 10 - 0

P = 10.

So the maximum willingness to pay is equal to 10.

So the formula for consumer surplus becomes,

CS = 1/2 × (10 - P) × Q --------(1)

Now putting the values in our formula the consumer surplus at price $7 is equal to,

Consumer surplus = 1/2 × (10 - 7) × 3

Consumer surplus = 1/2 × 3 × 3

Consumer surplus = 9/2

CS = $4.5

Now when the price is equal to $5. Quantity demanded at this price will be equal to,

Q = 10 - P

Q = 10 - 5

Q = 5.

Putting in the Values in equation (1) we get,

CS = 1/2 × (10 - 5) × 5

CS = 1/2 × 5 × 5

CS = 25/2 = $12.5

Now when the price is equal to $3. The quantity demanded at this price will be equal to,

Q = 10 - P

Putting P = $3 we get,

Q = 10 - 3

Q = 7

Now putting the values in equation (1) we get,

CS = 1/2 × (10 - 3) × 7

CS = 1/2 × 7 × 7

CS = 49/2 = $24.5

2. Now the formula to calculate the producers surplus is given by,

Producers surplus = 1/2 × (price - price at 0 quantity supplied ) × quantity supplied

Let's calculate the price at 0 quantity.

Supply function is given as,

P = 2 + 0.5Q

Putting Q = 0, we get

P = 2 + 0.5×0

P = $2

So the price at 0 quantity supplied is equal to 2.

So the formula for calculating producers surplus becomes,

PS = 1/2 × (P - 2) × Q -----------(2)

Now the price is given as $7. Putting P = $7 quantity supplied will be equal to.

7 = 2 + 0.5Q

0.5Q = 7 - 2

0.5Q = 5

Q = 5/0.5

Q = 10

So quantity supplied is equal to 10.

Putting the values in equation (2) we get,

PS = 1/2 × (7 - 2) × 10

PS = 1/2 × 5 × 10

PS = $25

Now the price is equal to $5. The quantity supplied will be equal to,

5 = 2 + 0.5Q

0.5Q = 5-2

Q = 3/0.5 = 6

So quantity supplied is equal to 6.

Putting the values in equation (2) we get,

PS = 1/2 × (5 - 2) × 6

PS = 1/2 × 3 × 6

PS =$9.

Now when the price is equal to $3 quantity supplied will be equal to,

3 = 2 + 0.5Q

0.5Q = 3-2

0.5Q = 1

Q = 1/0.5 = 2

So the Quantity supplied is equal to 2.

Now putting the values in equation (2) we get,

PS = 1/2 × (3 - 2) × 2

PS = 1/2 × 1 × 2

PS = $1

I hope I was able to help you, thank you.