Final answer:
To calculate the consumer surplus, we need to find the area above the market price and below the demand curve. The demand equation is q = 20 - 0.05p^2, and the given unit price is p = 4. By integrating the demand function from p = 4 to the equilibrium price, we can find the consumer surplus. The consumer surplus at p = 4 is approximately $127.64.
Step-by-step explanation:
To calculate the consumer surplus at the indicated unit price p, we need to find the area above the market price and below the demand curve. The demand equation is q = 20 - 0.05p^2. We are given that p = 4. To find the consumer surplus, we need to integrate the demand function from p = 4 to the equilibrium price.
First, let's find the equilibrium price by setting the demand equation equal to zero: 20 - 0.05p^2 = 0. Solving for p, we get p = √(20/0.05) ≈ 14.14.
Next, we integrate the demand function from p = 4 to p = 14.14 to find the consumer surplus. The integral of the demand function is given by the antiderivative: ∫(20 - 0.05p^2) dp = 20p - 0.05(p^3/3). Evaluating the integral from p = 4 to p = 14.14, the consumer surplus is approximately $127.64.