Question

Answer all parts of 1 and then question 2 please. I am confused. On both of these questions.

The current toll for the use of a certain toll road is $1.75. A study conducted by the state highway department determined that, with a toll of p dollars, q cars will use the road each day, where q = 40,000 e - 0.4p, Is demand elastic or inelastic at p = 1.75? To determine if demand is elastic or inelastic, the elasticity must be computed. To compute the elasticity of demand for the given equation, use the formula for elasticity. What is the formula for elasticity? OA E(p) pf(p) f'(p) pf(p) f'(p) OBE(p) C. Elp) pf (p) fp) pf (p) f(p) D. Elp) Notice that f(p)=q = 40,000 e - 0.4P is given in the problem statement, but I'(p) is not. Calculate f'(p). f'(o) - d (40,000 -0.4p) dp

Answer 1

1) Derivative of a equation is calculated as: (dq / dp) * (p / q)

where (dq / dp) is the derivative of "q / f(p)" with respect to "p"

f'(p) = (dq / dp)

Thus, elasticity = pf'(p) / f(p)

Option C is correct.

q = 40,000 * e^^-0.4p

(dq / dp) = 40,000 * e^^-0.4p * (-0.4) = -16,000 * e^^-0.4p

At p = 1.75

(dq / dp) = -16,000 * e^^-0.4p = -7,945.37

2) q = 344 - p

At p = 103, q= 241

Elasticity of demand = (dq / dp) * (p / q)

(dq / dp) = -1

Elasticity of demand = -1 * (103 / 241) = -0.43