Question

Suppose the market demand for a good is described by the demand function P = 160 - 2Q. It follows that the total revenue function relating the total revenues (TR) to the quantity sold (Q) is:

Answer 1

The total revenue function, given the demand function P = 160 - 2Q, is TR = 160Q - 2Q^2. This function demonstrates how total revenue relates to the quantity sold. Graphical visualization can also be used to determine the equilibrium price and quantity.

Step-by-step explanation:

The student is asking for the total revenue function based on a given market demand equation. The demand function is P = 160 - 2Q, where P is the price and Q is the quantity. Total revenue (TR) is calculated by multiplying the price by the quantity sold, so the total revenue function TR can be expressed as TR = P × Q. Substituting the demand function into this equation gives us TR = (160 - 2Q) × Q, which simplifies to TR = 160Q - 2Q2. This quadratic equation represents how total revenue changes with the quantity sold.

Solving models with graphs is an alternative way if algebra is challenging. By graphing the demand and supply equations, the equilibrium price and quantity where Qd equals Qs can be visualized where the demand and supply curves intersect. For detailed calculations, algebraic manipulation can reveal the same equilibrium point, as shown by the equations that involve solving for P.