The demand function for a product is modeled by

Question

p=20-0.02x,0<x<2000

where P is the price (in dollars) and x is the number of units. Determine the demand is inelastic

Answer 1

p=20-.02x

p= 20 - x/50

0<x<2000, but really it's 0<x<1,000 as price would be negative if x>1000. You'd have to pay people to take the product away, for x>1000

price elasticity of demand = % change in quantity demanded divided by % change in price

change in x divided by x all over change in p divided by p

graph the equation, It's x intercept is (1,000, 0). The y intercept is (0,20)

connect them with a straight line. The midpoint of that line segment is (500,10)

the elasticity of demand at the midpoint is -1, but the negative sign is traditionally dropped, and the point elasticity of demand at the midpoint is unit elastic = 1

at points higher on the demand curve, above the midpoint, the price elasticity is elastic, >1

at points lower on the demand curve, below the midpoint, the price elasticity is inelastic, <1

the demand curve is inelastic when price is lower than $10

but this apparently is a calculus question, so:

point price elasticity of demand = (dx/dp)(p/x)

the derivative of x with respect to p, times p/x

p=20-x/50

50p = 1000-x

x = 1000-50p

x' = dx/dp = -50

Ed = Elasticity of demand = (x')(p/x) = -50p/x

at the midpoint (500,10) Ed= -50(10)/500 = -1 or 1 when the sign is dropped

at points below price = $10, and consumers buying more than 500, the demand curve is price inelastic