U = 4x11/2 + 2x2. p1 = 12 and p2 = 8. Income (m) is 173.16....

Question

Question

U = 4x11/2 + 2x2. p1 = 12 and p2 = 8. Income (m) is 173.16. The utility optimizing quantity of x2 is

Answer 1

Answer #1

At optimal; MRS = p1/p2

MRS = MU_x1/MU_x2

MU_x1 = 4 * 1/2 x1^(-1/2) = 2/(x1)^1/2

MU_x2 = 2

So, (2/(x1)^1/2)/2 = 12/8

1/(x1)^1/2 = 12/8

(x1)^1/2 = 8/12 = 2/3 = 0.67

x1 = 0.45

Budget line: p1x1 + p2x2 = m

12x₁ + 8x₂ = 173.16

12(0.45) + 8x₂ = 173.16

8x₂ = 173.16 - 5.4

x₂ = 20.97

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Answer 2

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