Suppose the following information is known about a market: 1. Sellers

Suppose the following information is known about a market:

1. Sellers will not sell at all below a price of $2.
2. At a price of $10, any given seller will sell 10 units.
3. There are 100 identical sellers in the market.

Assuming a linear supply curve, use this information to derive the market supply curve.

ANSWER

First, Q = 100q since all firms are identical. This gives two points: (p = 2, Q = 0 ) and
(p = 10, Q = 1000 ). From the first point, it is known that p = 2 + bQ. When Q = 1000, 10 = 2 + b(1000 ). Solving for b yields b = .008. Rearranging to solve for Q yields: Q = -250 + 125p or P= 2 + .008Q.