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Given the following demand function;
= − . + . − , and
= , = , = =
Where Qx= Quantity of good X, Px= Price of good X, Y= the income of the individual and Py= the price of good Y. Calculate;
A. The price elasticity of demand of good X and interpret your result.
B. The income elasticity of demand of good X and interpret your result.
C. The cross-price elasticity of good X for good Y and interpret your result.

Sagot :

panisumi

A. The price elasticity of demand of good X can be calculated using the formula:

\[ \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} \times \frac{\text{Price of Good X}}{\text{Quantity of Good X}} \]

Given the demand function, Qx = 300 - 2Px + 0.5Y - 0.2Py, the price elasticity of demand for good X is:

\[ \text{PED}_{X} = \left( \frac{-2}{300 - 2PX + 0.5Y - 0.2PY} \right) \times \left( \frac{PX}{300} \right) \]

Interpretation: The price elasticity of demand for good X will determine the sensitivity of the quantity demanded of good X to changes in its price. If the calculated price elasticity of demand for good X is greater than 1, it signifies that the demand for good X is elastic, meaning a change in price will lead to a proportionally larger change in quantity demanded. If less than 1, it indicates inelastic demand, where quantity demanded changes proportionally less with price changes.

B. The income elasticity of demand of good X can be calculated using the formula:

.

Interpretation: The income elasticity of demand for good X will show the impact of changes in consumer income on the quantity of good X demanded. If the calculated income elasticity is positive, it indicates that good X is a normal good, meaning as income increases, the quantity demanded of good X also increases. A negative income elasticity suggests that good X is an inferior good, where an increase in income leads to a decrease in the quantity demanded of good X.

C. The cross-price elasticity of good X for good Y can be calculated using the formula:

[tex]\[ \text{CPE}_{XY} = \left( \frac{-0.2}{300 - 2PX + 0.5Y - 0.2PY} \right) \times \left( \frac{PX}{300} \right) \]

[/tex]

Interpretation: The cross-price elasticity of demand for good X with respect to the price of good Y will determine if the two goods are substitutes or complements. A positive cross-price elasticity indicates that the goods are substitutes, meaning an increase in the price of good Y leads to an increase in the quantity demanded of good X. A negative cross-price elasticity suggests that the goods are complements, where an increase in the price of good Y results in a decrease in the quantity demanded of good X.

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