Consider a market with one buyer with a fixed demand and multiple sellers for a divisible good. The goal of the market is to determine a uniform unit-price for the good as well as which seller supplies what quantity of the good.
There are two types of sellers:
- Quoters are able to provide to the market their desired price and quantity for supplying part of the divisible good;
- Price takers have private prices and quantities. If the (uniform) market price is above their private prices, they are ready to provide at most their quantities, otherwise they do not provide anything.
The challenge here is how to derive market price.
If have thought about the following two-stage process:
- Get quoters' quote
- Derive market price (how demand should be fixed at this stage since full supply curve is not know?)
- Let price takers supply some quantity or not
If it helps, a reasonable assumption would be that price takers submit their quantities (but not their prices) to the market.
I am looking for any reference or thoughts that would allow to address this problem or a similar one.