400 For the demand function q Dx find the following a The

400 For the demand function q = D(x) =-, find the following. a) The elasticity b) The elasticity at x 7, stating whether the demand is elastic, inelastic, or has unit elasticity c) The value(s) of x for which total revenue is a maximum (assume that x is in dollars) a) Find the equation for elasticity. b) Find the elasticity at the given price, stating whether the demand is elastic, inelastic, or has unit elasticity. E(7) (Simplity your answer. Type an integer or a fraction.) is the demand at x = 7 elastic, inelastic, or does it have unit elasticity? O A. unit elasticity OB. elastic O c. inelastic Click to select your answer(s)

Solution

a)

given q=D(x) =400_/x

=>dq_/dx =-400_/x²

E(x)=(dq_/dx)*(x_/q)

E(x)=(-400_/x²)*(x_/(400/x))

E(x)=(-400_/x²)*(x²_/400)

E(x)=-1

b)

at x =7, E(7)=-1

|E(7)| =1

so the demand at x=7 have unit elasticity

c)

total revenue is constant for all values of x

=>the total revenue is independant of x

so,revenue =qx =400. its constant

please rate if helpful. please comment if you have any doubt