Question

8. A consumer spends all her income of Br120 on the two goods A and B. Good A costs Br 10 a unit and good B costs Br 15. What combination of A and B will she purchase if her utility function is U = 4A0.5B0.5,​

Answer 1

Explanation:

To find the combination of goods A and B that a consumer will purchase if she spends all her income of Br120 on these two goods and her utility function is U = 4A0.5B0.5, we can use the Lagrangian method.

The Lagrangian function is:

L = 4A0.5B0.5 + λ(120 - 10A - 15B)

where λ is the Lagrange multiplier.

Taking the partial derivative of L with respect to A and B and setting them equal to zero, we get:

∂L/∂A = 2A-0.5B0.5 - 2λ = 0

∂L/∂B = A0.5B-0.5 - 3λ/2 = 0

Solving for A and B, we get:

A = (15λ/8)^2

B = (10λ/8)^2

Substituting these values into the budget constraint, we get:

10A + 15B = 120

Solving for λ, we get:

λ = 16/3

Substituting this value of λ into the expressions for A and B, we get:

A = 45

B = 40

Therefore, the consumer will purchase 45 units of good A and 40 units of good B.

I hope this helps! Let me know if you have any other questions or if there is anything else I can help you with.