Question

Suppose the demand function for a firm’s product is given by:

lnQx = 3 – 0.5lnPx -2.5lnPy +lnM + 2lnA

where Px = GH¢10, Py = GH¢4, M = GH¢20,000 and A = GH¢250.

i. Determine the own price elasticity of demand, and state whether demand is elastic, inelastic or unitary elastic.
ii. Determine the cross-price elasticity of demand between good X and good Y, and state whether these two goods are substitutes of complements.
iii. Determine the income elasticity of demand, and state whether good X is normal or inferior good.
iv. Determine the own price elasticity of demand.

Answer 1

Answer on Question #79598, Economics / Macroeconomics

i. Own price elasticity of demand = $\Delta \ln Qx\Delta \ln Px$.

$$E = -0.5$$

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

ii. Cross price elasticity $E_c = \Delta Ln Qx / \Delta Ln Py$.

$$E_c = -2.5$$

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.

iii. Income elasticity $Em = \Delta Ln Qx / \Delta Ln M$.

$$Em = 1$$

Positive sign shows that the good $X$ is a normal good.

iv. Advertising elasticity $E_a = \Delta Ln Qx / \Delta Ln A$.

$$E_a = 2$$

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.

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https://www.investopedia.com/terms/d/demand-elasticity.asp

https://financetrain.com/demand-function-and-demand-curve/