Question

Consider the utility function of U(X,Y) =

X2Y2.
What is the own-price elasticity for Marshallian Demand X?

Answer 1

The own-price elasticity for Marshallian Demand X can be calculated using the equation: Own-price elasticity = (% change in quantity demanded)/(% change in price). The own-price elasticities for Marshallian Demand X are not the same. The elasticity of demand changes as the price changes.

Step-by-step explanation:

The own-price elasticity for Marshallian Demand X can be calculated using the equation:

Own-price elasticity = (% change in quantity demanded)/(% change in price)

Let's calculate the elasticity of demand as the price falls from 5 to 4:

1. Initial price (P1) = 5
2. Final price (P2) = 4
3. % change in price = (P2 - P1)/P1 * 100% = (4 - 5)/5 * 100% = -20%
4. Initial quantity demanded (Q1) can be found by substituting P1 in the demand equation: P1 = 2/Q1 → 5 = 2/Q1 → Q1 = 2/5
5. Final quantity demanded (Q2) can be found by substituting P2 in the demand equation: P2 = 2/Q2 → 4 = 2/Q2 → Q2 = 2/4 = 1/2
6. % change in quantity demanded = (Q2 - Q1)/Q1 * 100% = ((1/2) - (2/5))/(2/5) * 100% = -20%
7. Therefore, the own-price elasticity for Marshallian Demand X as the price falls from 5 to 4 is:

Own-price elasticity = (% change in quantity demanded)/(% change in price) = -20%/-20% = 1

Now let's calculate the elasticity of demand as the price falls from 9 to 8:

1. Initial price (P1) = 9
2. Final price (P2) = 8
3. % change in price = (P2 - P1)/P1 * 100% = (8 - 9)/9 * 100% = -11.11%
4. Initial quantity demanded (Q1) can be found by substituting P1 in the demand equation: P1 = 2/Q1 → 9 = 2/Q1 → Q1 = 2/9
5. Final quantity demanded (Q2) can be found by substituting P2 in the demand equation: P2 = 2/Q2 → 8 = 2/Q2 → Q2 = 2/8 = 1/4
6. % change in quantity demanded = (Q2 - Q1)/Q1 * 100% = ((1/4) - (2/9))/(2/9) * 100% = -36.36%
7. Therefore, the own-price elasticity for Marshallian Demand X as the price falls from 9 to 8 is:

Own-price elasticity = (% change in quantity demanded)/(% change in price) = -36.36%/-11.11% = 3.27

As we can see, the own-price elasticities for Marshallian Demand X are not the same. The elasticity of demand changes as the price changes.