Suppose a market with two sellers
Seller 1 has a marginal cost of c1=20q1 and seller 2 has a marginal cost of c2=40q2
Find the market supply curve in a competitive market where the price = c1= c2
To find the market supply curve in a competitive market where the price equals the marginal costs of both sellers, we need to determine the quantities that each seller is willing to supply at that price point.
Given that the price is equal to the marginal cost:
P = c1 = 20q1
P = c2 = 40q2
We can equate these two equations:
20q1 = 40q2
To find the relationship between q1 and q2, we need to solve this equation for one variable in terms of the other.
Divide both sides of the equation by 20:
q1 = 2q2
Now we have a relationship between the quantities that each seller is willing to supply. Let's express this in terms of only one variable:
q2 = 0.5q1
Now, we can express the total market supply in terms of q1:
Q = q1 + q2
Q = q1 + 0.5q1
Q = 1.5q1
So, the market supply curve in this competitive market is given by:
Q = 1.5q1
This equation shows the relationship between the total quantity supplied in the market and the quantity supplied by seller 1 (q1) under the condition that the price equals the marginal costs of both sellers.