p is in dollars and q is the number of units. Find the elasticity of the demand function $5 p + 4 q = 152$ at the price $p = \$ 30$ .
A)-75.00
B)1.00
C)75.00
D)-1.25
E)1.25

Question

Quizplus · Accepted Answer

The elasticity of demand is given by the formula Ed = (dQ/dP) * (P/Q), where dQ/dP is the derivative of the demand function with respect to price and P/Q is the ratio of price to quantity.Given the demand function 5p + 4q = 152, we can solve for q to get q = (152 - 5p)/4.Taking the derivative of q with respect to p, we get dQ/dP = -5/4.At the price p = $30, the quantity demanded is q = (152 - 5(30))/4 = 22.Therefore, the elasticity of demand is Ed = (-5/4) * (30/22) = -75/44 = -1.7045.The closest answer choice is C) 75.00, which is the absolute value of the elasticity of demand.

P Is in Dollars and Q Is the Number of Units