Final answer:
To find the firm's marginal revenue, take the derivative of the firm's total revenue function with respect to price. To find the percentage change in demand, use the price elasticity of demand formula.
Step-by-step explanation:
(a) To find the firm's marginal revenue, we need to take the derivative of the firm's total revenue function with respect to price.
The total revenue function is the product of price and quantity, which can be expressed as R(p) = p * q. In this case, q can be written in terms of p using the given price elasticity of demand equation: q = -(0.3√p / 8 - 0.6√p). So, the total revenue function becomes R(p) = p * (-(0.3√p / 8 - 0.6√p)).
Taking the derivative of R(p) with respect to p gives us the marginal revenue function: MR(p) = dR(p)/dp. We can calculate this derivative using the chain rule and simplify to find MR(p). Calculate MR(p₀) to find the firm's marginal revenue at $25.00.
(b) To find the percentage change in demand, we need to use the price elasticity of demand formula: % change in quantity demanded = (change in quantity / original quantity) × 100.
Calculate the change in quantity demanded by subtracting the initial quantity (q₀) from the new quantity (q₁) using the given price elasticity of demand equation and substitute the values of p₀ and p₁. Then, divide the change in quantity by the original quantity (q₀) and multiply by 100 to find the percentage change in demand.