You run a small classroom market experiment with only three buyers and three sellers. The willingness to pay (reservation value) for buyer A is $7; for buyer B it is $5; and for buyer C it is $3. The willingness to accept (reservation value) for seller X is $2; for seller Y it is $4; and for seller Z it is $6.
a. Sketch the supply and demand in this market.
b. What is the equilibrium quantity?
c. What is the social surplus given this outcome?
a. To sketch the supply and demand in this market, we can plot the reservation values on a graph. The demand curve represents the willingness to pay for each buyer, and the supply curve represents the willingness to accept for each seller.
On the graph, we can plot the quantity on the x-axis and the price on the y-axis. The demand curve would start at a price of $7 and quantity 0, and slope downwards to a price of $3 and quantity 3. The supply curve would start at a price of $2 and quantity 0, and slope upwards to a price of $6 and quantity 3.
Supply Curve
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Demand Curve
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Quantity
b. The equilibrium quantity is the quantity at which the demand and supply curves intersect. In this case, the equilibrium quantity is 1, where the demand curve and supply curve intersect.
c. To calculate the social surplus, we need to find the area of the triangle above the equilibrium quantity and below the demand curve. The social surplus is the total willingness to pay minus the total willingness to accept.
For buyer A, the surplus is the difference between their willingness to pay ($7) and the equilibrium price ($4) multiplied by the quantity (1), which is 7 - 4 = $3.
For buyer B, the surplus is the difference between their willingness to pay ($5) and the equilibrium price ($4) multiplied by the quantity (1), which is 5 - 4 = $1.
For buyer C, their willingness to pay is lower than the equilibrium price, so their surplus is 0.
The total social surplus is the sum of the individual surpluses, which is $3 + $1 + 0 = $4. Hence, the social surplus given this outcome is $4.
a. To sketch the supply and demand in this market, we can plot the demand curve and the supply curve.
The demand curve represents the maximum price a buyer is willing to pay at each quantity. In this case, we have three buyers with different reservation values:
Buyer A ($7) \
Buyer B ($5) | Demand Curve
Buyer C ($3) /
The supply curve represents the minimum price a seller is willing to accept at each quantity. In this case, we have three sellers with different reservation values:
Seller X ($2) \
Seller Y ($4) | Supply Curve
Seller Z ($6) /
b. The equilibrium quantity is the quantity at which the quantity demanded is equal to the quantity supplied. To find this, we can compare the reservation values of the buyers and sellers.
Buyer A ($7) \
Buyer B ($5) | Equilibrium Quantity
Buyer C ($3) /
Seller X ($2) \
Seller Y ($4) |
Seller Z ($6) /
From the above sketch, we can see that at a price of $4, the quantity demanded by buyers is equal to the quantity supplied by sellers. Therefore, the equilibrium quantity is 1.
c. Social surplus is the total value created for both buyers and sellers in a market. It can be calculated by finding the area between the demand and supply curves up to the equilibrium quantity.
In this case,
Buyer A ($7) \
Buyer B ($5) | Social Surplus
Buyer C ($3) /
Seller X ($2) \
Seller Y ($4) |
Seller Z ($6) /
Since the equilibrium quantity is 1, the social surplus can be calculated as the difference between the maximum reservation value of the buyers (Buyer A - $7) and the minimum reservation value of the sellers (Seller X - $2). Therefore, the social surplus is $7 - $2 = $5.
a. To sketch the supply and demand in this market, we need to plot the buyers' willingness to pay (demand) and the sellers' willingness to accept (supply) on a graph.
First, let's plot the demand curve. We have three buyers with different reservation values. Buyer A's willingness to pay is $7, buyer B's is $5, and buyer C's is $3. We'll plot these points on the graph, with the quantity on the x-axis and the willingness to pay on the y-axis. Connect these points to create the demand curve, which should slope downwards.
Next, let's plot the supply curve. We have three sellers with different reservation values. Seller X's willingness to accept is $2, seller Y's is $4, and seller Z's is $6. Plot these points on the graph, with the quantity on the x-axis and the willingness to accept on the y-axis. Connect these points to create the supply curve, which should slope upwards.
b. The equilibrium quantity is the quantity at which the demand and supply curves intersect. It represents the quantity where buyers are willing to pay exactly as much as sellers are willing to accept. In this case, the equilibrium quantity is where the demand curve and supply curve intersect on the graph.
c. To calculate the social surplus, we need to find the area between the demand and supply curves up to the equilibrium quantity. This represents the additional benefit (consumer surplus) from buyers paying less than their reservation value, as well as the additional benefit (producer surplus) from sellers receiving more than their reservation value.
To calculate the social surplus, we need to calculate the consumer surplus and the producer surplus separately, and then sum them.
Consumer Surplus: To calculate the consumer surplus, find the difference between each buyer's reservation value and the equilibrium price, and sum those differences.
- For buyer A: Consumer surplus = Reservation value - Equilibrium price = $7 - Equilibrium price
- For buyer B: Consumer surplus = Reservation value - Equilibrium price = $5 - Equilibrium price
- For buyer C: Consumer surplus = Reservation value - Equilibrium price = $3 - Equilibrium price
Producer Surplus: To calculate the producer surplus, find the difference between each seller's reservation value and the equilibrium price, and sum those differences.
- For seller X: Producer surplus = Equilibrium price - Reservation value = Equilibrium price - $2
- For seller Y: Producer surplus = Equilibrium price - Reservation value = Equilibrium price - $4
- For seller Z: Producer surplus = Equilibrium price - Reservation value = Equilibrium price - $6
Once you have calculated the consumer surplus and producer surplus, sum them up to find the social surplus.