Question

The following questions are worth 6 points each. 21) Solve the following utility function to be optimized. Only consider they are looking for an interior solution: (10pts) U(X1,x2) = 1 ln(x) + 2 In(x2) MU(x)= 1/ MU(X) = 2/2 Subject to the budget constraint: 500 = 2 + xy +4.X2 a. Find the optimal consumption bundle. (4 pts) b. Find the utility at this point. (1 pt) C. Show work (5 pts) u (x,x) = 1 in (X.) + 2 In (x2) mu (x2) = 2/2

Answer 1

21.

Ans:

In equilibrium, we have:

$MRS=\frac{MU(x_{1})}{MU(x_{2})}=\frac{1/x_{1}}{2/x_{2}}=\frac{x_{2}}{2x_{1}}=\frac{P_{1}}{P_{2}}=\frac{2}{4}$

$x_{1}=x_{2}$

Using this in budget, we get:

$500=2x_{1}+4x_{1}=6x_{1}$

Optimal bundle

$x_{1}=\frac{500}{6}=x_{2}$

Utility at this point:

$U=ln(500/6)+2ln(500/6)=3ln(500/6)=13.27$

If you are satisfied with the answer, please provide a positive rating. Feel free to comment in case of queries.

Have a nice day ahead!