Question 2: Suppose Vivian has a utility function U = X^0.4Y^0.6, which X and Y

Question

Question 2:

Suppose Vivian has a utility function U = X^0.4Y^0.6, which X and Y are two goods. The prices for X and Y are $4 and $6, respectively. She has $100 in her pocket. (a) Please explain why Vivian's utility function is a special case of Cobb-Douglas function. (b) Please write down Vivian's budget constraint to buy both goods. (c) Please find the optimal quantities of X and Y when Vivian has achieved her maximal utility level given her budget constraint. (d) Please find the MRS_XY given by MU_X/MU_Y = 2/3.

Explanation / Answer

Vivian has a utility function where alpha(power of X) and beta(power of Y) is 0.4 and 0.6 both of which sums equal to 1. And same is the form of a cobb douglas utility function. Where we have, the power of one element as a and the other as 1-a.

b.. Budget constraint for Vivian:

4 X + 6Y = $100

c. The condition for equilibrium is given by MUx/MUy = Px/Py which implies that (0.4 X -0.6 Y0.6 ) / (0.6 X0.4 Y-0.4) = 4/6

or (X/Y) 10 = 1

Solve for this condition and the budget constraint

You will get the answers for X and Y or alternatively you can use the lagrangian methods also.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.