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.

Question

a. Sketch the supply and demand in this market.
b. What is the equilibrium quantity?
c. What is the social surplus given this outcome?

Answer 1

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.