Inverse Demand Function and the Law of Demand

Finding and Confirming the Quantity that Maximizes Consumer Surplus

Calculating Consumer Surplus from a Demand Function

A market has an inverse demand function given by P = 50 - 2Q, where P is the price and Q is the quantity. If the market price is set at P = 10, what is the total consumer surplus?

Interpreting the Integral for Consumer Surplus

Analyzing an Incorrect Consumer Surplus Calculation

The total consumer surplus in a market can be calculated using the mathematical expression $\int_{0}^{Q_0} (f(q) - P_0) \,dq$. Match each component of this expression to its correct economic interpretation.

Evaluating Calculation Methods for Consumer Surplus

A market is characterized by an inverse demand function given by P = 144 - Q², where P is the price and Q is the quantity. If the product is sold at a market price of $80, the correct upper limit of integration (Q₀) needed to calculate the total consumer surplus is ___.

Evaluating Methods for Calculating Consumer Surplus

Consider a market where consumer surplus is calculated using a definite integral based on the inverse demand function and the market price. True or False: If the market price of the product increases, while the demand function remains unchanged, the value of the integrand (the function being integrated) will decrease for every quantity level considered in the calculation of the new consumer surplus.

Suppose that for a particular good, the total area under the inverse demand curve from a quantity of 0 to 50 units is calculated to be $2,500. This figure represents the total value consumers receive from consuming those 50 units. If the market price for the good is$35 per unit and 50 units are sold, what is the total consumer surplus?