Final answer:
The elasticity of demand, E, for the function q=37,100-2p², is determined by the formula E = (p/q) × (dq/dp). Total revenue is maximized at the price level where the derivative of the revenue function is zero. Without specific price values, we cannot calculate the exact E or the maximizing q value.
Step-by-step explanation:
The question asks to determine the elasticity of demand, E, for the given function q=37,100-2p², and to find out the values of q at which total revenue is maximized. To find the elasticity of demand, we would compute the percentage change in quantity demanded due to a change in price. Elasticity can be defined as elastic (E > 1), unitary (E = 1), or inelastic (E < 1), and it helps in deciding whether to increase or decrease the price of a product to maximize revenue.
In general, the formula for percentage change in quantity demanded is [(change in quantity) / (original quantity)] × 100. However, to determine E for a quadratic demand function, one would typically differentiate the demand function with respect to price and then apply the elasticity formula: E = (p/q) × (dq/dp). Without specific prices, we cannot find the exact values of E for this function. Total revenue (R) can be found by multiplying the quantity (q) by the price (p), and R is maximized where the derivative of the revenue function (dR/dp) is equal to zero, indicating the highest possible revenue at a certain price level.