Final answer:
The own price elasticity of demand for the firm's product, based on the given demand function and values, is approximately -0.000244, indicating that demand is inelastic regarding its price.
Step-by-step explanation:
The student asked to determine the own price elasticity of demand for a firm's product based on the demand function 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); and given values Px = K10, Py = K4, M = K20000, and A = K250.
Own price elasticity of demand measures how much the quantity demanded of a good responds to a change in the price of that good. It is calculated using the formula:
Elasticity = (Percentage change in quantity demanded) / (Percentage change in price)
The coefficient of Px in the demand function (-0.5) represents the change in quantity demanded for each one-unit change in price. Hence, the own price elasticity of demand at the given price (Px = K10) can be computed as:
Elasticity = (Px/Qd) * (-0.5)
First, we need to calculate Qd by substituting the given values into the demand function:
Qd = 3 – 0.5(10) – 2.5(4) + 20000 + 2(250)
Qd = 3 – 5 – 10 + 20000 + 500
Qd = 20488
So, the own price elasticity of demand is:
Elasticity = (10 / 20488) * (-0.5)
Elasticity = -0.5 / 2048.8
Elasticity ≈ -0.000244
This means that the demand is inelastic with respect to its own price.