Question

The market demand for commodity X is given by:

QXD = 2,000 – 0.5PX1/2 + 8PY1/2 – 5I + AX + 2.5POP,

where QXD is the quantity demanded for X, PX is the price of X, PY is the price of Y, I is income, AX is advertising expenditures on X, and POP is population. Suppose we know that PX is 100, PY is 50, I is 100, AX is 20, and POP is 40.

Calculate the own-price demand elasticity. Is demand elastic or inelastic? Interpret your result.

Answer 1

QXD = 2,000 - 0.5PX^1/2 + 8PY^1/2 - 5I + AX + 2.5POP

Plugging in given values,

QXD = 2,000 - 0.5 x (100)^1/2 + 8 x (50)^1/2 - (5 x 100) + 20 + (2.5 x 40)

QXD = 2,000 - (0.5 x 10) + (8 x 7.07) - 500 + 20 + 100

QXD = 1,620 - 5 + 56.56

QXD = 1,671.56

Own-price elasticity = (dQXD / dPX) x (PX / QXD)

= - [0.5 x (1/2) / (PX^1/2)] x (PX / QXD)

= (- 0.25 / 10) x (100 / 1,671.56)

= - 0.015

Since absolute value of elasticity is less than 1, demand is inelastic. The elasticity value signifies that as PX rises (falls) by 1%, quantity demanded (DX) falls (rises) by 0.015%.