Final answer:
The inverse demand function p(y) for a monopoly is p=10-0.5y, which can be found by rearranging the original demand equation. Graphical methods can also be used to determine equilibrium price and quantity, and if profit-maximizing price falls below average variable cost, the firm should supply zero output.
Step-by-step explanation:
The student's question is about finding the inverse demand function, p(y), for a monopoly with a given demand function y=20−2p, where p is the price and y is the quantity demanded.
To find the inverse demand function, we need to solve for p as a function of y. Starting with the original demand function y=20−2p, we solve for p to get p=10−0.5y. This equation represents the inverse demand function, or the price as a function of the quantity.
Graphical representation can also be used to find the equilibrium price and quantity. By plotting both the demand curve (P = 8 - 0.5Qd) and the supply curve (P = -0.4 + 0.2Qs), we can determine the point where these curves intersect.
At this intersection, the quantity supplied equals the quantity demanded, and the equilibrium price can be determined. For example, with a price of $2, the quantity supplied and demanded is 12, confirming our algebraic calculations.
If a monopoly's profit-maximizing price falls below the average variable cost, the firm should not supply any output, as it would incur losses on each unit produced. Graphically, this situation is indicated by a demand curve intersecting the average variable cost curve below the price level that would allow the firm to cover its variable costs.