Question

Suppose the demand function for a firm’s product is given by Qd = 3 – 0.5Px – 2.5Py + M + 2A Where Px is the commodity price, Py is the price of a related commodity, M is per capita disposable income, and A is advertising expenditure (thousand Kwachas); Px = K10, Py = K4, M = K20000, and A = K250. a) Determine the own price elasticity of demand, and state whether demand is?

Answer 1

The price elasticity of demand measures how quantity demanded responds to price changes, and the formula is (ΔQ/Q) / (ΔP/P). Calculations yield different elasticities because the demand curve P=2/Q is non-linear. Elasticity will differ as prices change.

Step-by-step explanation:

When calculating price elasticity of demand, it's important to understand that it measures the responsiveness of the quantity demanded to a change in price. For the demand curve P = 2/Q, we can calculate the elasticity at different price levels. As price falls from 5 to 4 and from 9 to 8, the elasticity calculations will yield different results due to the demand curve's non-linear nature.

At a price of 5, the quantity demanded (Q) is 0.4 (since P=2/Q gives us Q=2/5). When the price drops to 4, the quantity demanded increases to 0.5. The formula for elasticity is (ΔQ/Q) / (ΔP/P), which in this case becomes

((0.5 - 0.4) / 0.4) / ((4 - 5) / 5) = 0.25 / -0.2 = -1.25. The negative sign indicates that the direction of the change is opposite that of the price change, which is typical for demand curves.

Similarly, when price drops from 9 to 8, we perform the same calculation using the new quantities obtained from P=2/Q. The quantities are approximately 0.222 and 0.25 respectively, which provides us with a different elasticity value.

The price elasticity of demand changes depending on the price level on the demand curve due to its curvature; therefore, we would not expect the elasticity to be the same for different price changes.