Reservation Prices

1. Reservation Prices

2. P S1 P1 D1 Q Q1

3. Before we saw that when we have supply and demand together in a market the equilibrium occurred where the supply and the demand curve cross. The way we looked at this was to consider other prices. For example, at a price higher than P1 look at what is happening horizontally. The quantity supplied is greater than the quantity demanded and we said this created a force to push the price down to P1. Similarly, at a price below P1 the quantity demanded is greater than the quantity supplied and this creates a force to push the price up to P1. At P1 the Qd = Qs and thus there is no force for change. So from this horizontal view of the graph we have a theory of price change: surpluses, or excess supplies, push the price down and shortages, or excess demands, push the price up. Next, let’s take a different view of the market outcome. This time, we will take a vertical view. This will be another interpretation of the market outcome. Both views are happening simultaneously (at the same time).

4. P S1 Pbr P1 Psr D1 Q Q’ Q1

5. When you view the equilibrium vertically you see that each Q up to Q1 gets traded. Let’s see some new ideas by first observing what is happening at Q’, Notice at Q’ the demand curve height is labeled Pbr. This price is the highest price someone is willing to pay for this unit. How do I know this? Well, we assume the demand curve is real and at any other price higher than this we would see a lower quantity demanded. So, at Q’ the highest price that can be charged and have this unit demanded is Pbr. Pbr is called the buyer’s reservation price because it is the highest price the buyer would be willing to face and still call in a reservation to get the good. Note that each unit up to Q1 the reservation price is falling (and it falls after that as well). This is because not everyone values a good the same, and some people want more than 1 unit of a good per period of time, but typically the value of additional units are not as great as previous units and thus the reservation price falls. Also note that all Q1 units trade for P1 per unit, but the reservation price on all units up to Q1 is higher than P1. Buyer surplus on a unit is the buyer’s reservation price minus the actual selling price. On all units before Q1 buyer surplus is positive and on the last unit, Q1, the buyer surplus is 0.

6. Notice at Q’ the supply curve height is labeled Psr. This price is the lowest price someone is willing to accept for this unit and make the unit available for sale. How do I know this? Well, we assume the supply curve is real and at any other price lower than this we would see a lower quantity supplied. So, at Q’ the lowest price that can be charged and have this unit supplied is Psr. Psr is called the seller’s reservation price because it is the lowest price the seller would be willing to face and still call in a reservation to give up the good. Note that each unit up to Q1 the reservation price is rising (and it rises after that as well). This is because not everyone has the same cost in making the good, and some people want to sell more than 1 unit of a good per period of time, but typically the value of additional units cost more to make than previous units and thus the reservation price rises. Also note that all Q1 units trade for P1 per unit, but the seller reservation price on all units up to Q1 is lower than P1. Seller surplus on a unit is the actual selling price minus the seller’s reservation price. On all units before Q1 seller surplus is positive and on the last unit, Q1, the seller surplus is 0.

7. On any unit, total surplus = buyer surplus plus seller surplus. Note in the market 1) On all the units traded up to Q1, but not including Q1, total surplus is greater than 0. Plus both buyer and seller surplus are greater than 0. Both parties benefit from the trade. 2) On unit Q1, total surplus is zero and both buyer and seller surplus are 0. 3) On units above Q1, the units are not traded because the buyers and sellers have no room to negotiate on a price that would be agreeable to both. The smallest amount sellers need to get is higher than the amount buyers are willing to pay. IN this sense we say all mutually beneficial exchanges have taken place in the market and only those trades that are mutually beneficial have taken place.