Given the demand equation is 𝑥 = √100 − 3𝑝, find the elasticity of demand when price is price is 15. Is demand elastic or inelastic ?

To find the elasticity of demand, we first need to find the derivative of the demand function with respect to price (p). The demand function is given as x = √(100 - 3p).

Step 1: Differentiate the demand function with respect to p. The derivative of x with respect to p, dx/dp, is -3/(2√(100 - 3p)).

Step 2: Substitute the given price (p = 15) into the derivative. dx/dp at p = 15 is -3/(2√(100 - 3*15)) = -3/(2√(55)) = -3/14.8324 = -0.202.

Step 3: Calculate the elasticity of demand. The elasticity of demand (E) is given by the formula E = (dx/dp)(p/x). Substitute dx/dp = -0.202, p = 15, and x = √(100 - 315) = √55 = 7.416 into the formula. E = (-0.202)*(15/7.416) = -0.408.

Step 4: Determine whether demand is elastic or inelastic. If |E| > 1, demand is elastic. If |E| < 1, demand is inelastic. If |E| = 1, demand is unit elastic. Here, |E| = 0.408 < 1, so demand is inelastic.