Final answer:
The inverse demand curve derived from the demand equation q = 12 - 2p is p = 6 - 0.5q. This curve can be graphed along with the supply curve to find the equilibrium price and quantity where the curves intersect.
Step-by-step explanation:
To derive the inverse demand curve from the given demand equation, which is q = 12 - 2p, we need to solve for p (price) as a function of q (quantity).
The process involves rearranging the equation to solve for p. Starting from q = 12 - 2p, add 2p to both sides to get q + 2p = 12, and then subtract q from both sides to obtain 2p = 12 - q. Finally divide both sides by 2 to get p = 6 - 0.5q. Hence, the inverse demand curve is p = 6 - 0.5q.
When graphing supply and demand curves, typically, the price (P) is on the vertical axis and the quantity (Q) is on the horizontal axis to illustrate the relationship visually.
The negative slope of the inverse demand curve and the positive slope of the supply curve will intersect at the market equilibrium price and quantity where quantity demanded equals quantity supplied.
The inverse demand curve represents the relationship between the price and the quantity demanded, where the price is the independent variable and the quantity is the dependent variable. To find the inverse demand curve, we can rearrange the demand equation q = 12 - 2p:
p = (12 - q) / 2
The inverse demand curve is given by the equation p = (12 - q) / 2, which shows the price as a function of the quantity demanded.