The y-axis of the graph is named cost because it shows the total cost of producing a given quantity of a pure public good.
Why the y-axis is named cost not named marginal cost?
The y-axis of the graph is named cost because it shows the total cost of producing a given quantity of a pure public good. Marginal cost is the additional cost of producing one more unit of a good or service. In the case of a pure public good, the marginal cost of allowing one more person to consume the good is zero.
So, this is because the good is non-excludable, meaning that no one can be prevented from consuming it, and non-rivalrous, meaning that consumption by one person does not reduce the amount available to others.