Final answer:
The linear demand function D(p) for price P of pizzas can be rewritten from P = 8 - 0.5Qd to Qd = 16 - 2P. It shows a negative relationship between price and quantity demanded, indicating as price increases, demand decreases, and intersects with supply at the market equilibrium.
Step-by-step explanation:
If we assume demand is a linear function of the price, the demand function D(p) reflects the relationship between quantity demanded Qd and the price P. Given that the demand function is linear, we can express it in a slope-intercept form, which is a straight line equation typically represented as y = mx + b, where m is the slope and b is the y-intercept.
In the given context, the demand equation provided is P = 8 - 0.5Qd. This can be rewritten in terms of Qd as the subject, which results in the demand function Qd = 16 - 2P. In this function, the negative relationship between price and quantity demanded is captured by the negative coefficient of the price term, indicating that as price increases, the quantity demanded decreases.
When graphing supply and demand curves, it's evidenced by their intersection that equilibrium is achieved where Qs = Qd. In the scenario you've described, at a price of $2, the quantity supplied Qs equals the quantity demanded Qd, meaning that the market is in equilibrium with 12 personal pizzas being exchanged.