Question

For the following two demand functions, compute the four partial elasticities of demand and state whether the two commodities are substitutes or complements and the type of good (normal) given that Q1, Q2, P1, P2 > 0.

Q1 = 7 – 2P1 – P2
Q2 = 23 – P1 + 3P2
A) Calculate the elasticities and identify the relationship.
B) Calculate the elasticities but cannot determine the relationship.

Answer 1

To compute the partial elasticities of demand for the given demand functions, use the formulas, (P1/Q1) * (∂Q/∂P1) and (P2/Q1) * (∂Q/∂P2), to calculate E1, E2, E3, and E4. By computing the four partial elasticities, we can identify the relationship for part A and determine the elasticities without determining the relationship for part B.

Step-by-step explanation:

To compute the partial elasticities of demand for the given demand functions, we need to use the formula:

E = (∂Q/∂P) * (P/Q)

A)

For the first demand function Q1 = 7 – 2P1 – P2:

Partial Elasticity with respect to P1:

E1 = (∂Q1/∂P1) * (P1/Q1) = (-2) * (P1/(7 – 2P1 – P2))

Partial Elasticity with respect to P2:

E2 = (∂Q1/∂P2) * (P2/Q1) = (-1) * (P2/(7 – 2P1 – P2))

For the second demand function Q2 = 23 – P1 + 3P2:

Partial Elasticity with respect to P1:

E3 = (∂Q2/∂P1) * (P1/Q2) = (-1) * (P1/(23 – P1 + 3P2))

Partial Elasticity with respect to P2:

E4 = (∂Q2/∂P2) * (P2/Q2) = (3) * (P2/(23 – P1 + 3P2))

By computing the four partial elasticities using the respective formulas, we can identify the relationship.

B)

By calculating the four partial elasticities using the respective formulas, we can determine the elasticities but cannot determine the relationship between the two commodities.