Question

Imagine you consume two goods, K and L, and your utility function is U = K1/3L2/3. Your budget is $120; PK = $6; PL = $9. So, the optimal bundle for you to consume is (K = 6.6667, L = 8.8889). Now, suppose the price of good K increases to $9. The compensated price bundle is (K = 5.0976, L = 10.1952). What is the substitution effect on K?

Answer 1

- 1.5691 units

Step-by-step explanation:

Given that:

The utility function =
`K^(1/3)L^(2/3)`

Initial optimal bundle (K, L) = (6.6667, 8.8889)

Compensated price bundle (K, L) = (5.0976, 10.1952)

The Substitution effect reveals the relationship between the effect of change in relative price on goods demanded.

Thus, we can calculate the substitution effect on K by using the formula:

substitution effect on K = Compensated price bundle - Initial optimal bundle

substitution effect on K = 5.0976 - 6.6667

substitution effect on K = - 1.5691 units