Answer to Question #238403 in Microeconomics for Kuds

Question

Suppose the demand function for a firm's product is given by ௗ 𝑙𝑛𝑄௫ = 3 − 0.5 ln 𝑃௫ − 2.5 ln 𝑃௬ + ln 𝑀 + 2 ln 𝐴 Where Px is the price of the product = GHS 10 Py is the price of another product produced by the firm = GHS4 M is the income of consumers = GHS 20,000 and A is the expenditure on advertising for the product = GHS 250 a) Determine the own price elasticity of demand, and state whether the demand is elastic, inelastic or unitary elastic. b) Determine the cross-price elasticity of demand between good X and Y, and state whether the two goods are substitutes or complements. c) Determine the income elasticity of demand, and state whether the good X is a normal or an inferior good. d) Determine the own advertising elasticity of demand. 

Answer 1

a) Own price elasticity of demand = Δln QxΔln Px.

E = -0.5

Demand is inelastic because the absolute value of the elasticity is <0

b) Cross price elasticity Ec = ΔLn Qx/ΔLn Py.

Ec =-2.5

the two goods in question are substitutes. This is because a positive relation between the price of one and demand of the other proves the same. As the price of one increases, the other automatically becomes cheaper to buy and hence the demand increases.

c)Income elasticity Em = ΔLn Qx/Δ Ln M.

Em = 1

Positivesign shows that the good X is a normal good.

d) Advertising elasticity Ea = ΔLn Qx/Δ Ln A.

Ea = 2

Notice that the values of M, A or prices don't matter. What matters is the coefficients of the logarithm of these values, which is the partial derivatives.