How does the construction of a market demand curve for a private good differ from that for a public good?

The market demand curve of a private product is based on adding to each consumer's demand quantities at each price but by adding the price each consumer will be prepared to pay for every quantity of the product, the market demand curve for a public good will be determined.

The market demand curve for a private good is determined by adding up the quantities demanded by each consumer at each price but the market demand curve for a public good is determined by adding up the price each consumer is willing to pay for each quantity of the good.