Answer:
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.