Question

​Vasco's utility function​ is: Upper U equals 10 Upper X squared Upper ZU = 10X2Z The price of X is px​ = ​$55​, the price of Z is pz​ = ​$2020​, and his income is ​$150150. What is his optimal​ bundle? ​(round your answer to two decimal​ places)

Answer 1

Step-by-step explanation:

U = 10 X²Z

Given

150 = 5X + 20Z

30 = X + 4Z

To maximise utility

differentiating partially wrt X

MU_x = dU/ dX = 20XZ

differentiating partially wrt Y

MU_y = dU/dY = 10X²

For optimal bundle

MU_x / MU_y = P_x / P_y

20XZ / 10X² = 5 / 20

2Z / X = 1/4

X = 8Z

30 = X + 4Z

30 = 8Z + 4Z

12Z = 30

Z = 2.5

X = 8 X 2.5

= 20

X = 20

Z = 2.5