Question

Could someone help with this chart

The table below contains seven utility functions. For each utility function please compute the marginal utility with respect to X, and the marginal utility with respect to Xz. Use your expressions for the marginal utilities to find the marginal rate of substitution (MRS = Make sure you simplify the expression. Finally, state the level of utility for the consumption bundle (5,8) rounded to 1 d. You are not required to show your work in these questions. u(X, X2) MU,(2,22) MU,(X, X.) MRS u(5,8) 3x + 4x (x + 2)(5 + x) 3.x, +0.5% min(3x), 2x) Not applicable Not applicable Not applicable x1 + x3 Not applicable

Answer 1

dU MU:1 dri

$MU_{x2} = \frac{dU}{dx_2}$

$MRS = -\frac{MU_{x1}}{MU_{x2}}$

we will then plug x1 = 5 and x2 = 8 to get the utility corresponding to this bundle.

The table below has all the answers.

I am solving for first part :

U = 3x1+4x2 ; MU1 = 3 and MU2 = 4; MRS = -3/4

U(5,8) = 3*5+4*8=15+32=47

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u(x,x) MU(X) MU,(...) MRS (5,8) 3x + 427 3 4 -3/4 47 (5+x2)/(x1+2 (, + 2)(5 + x) 5+x2 x1 +2 91 4x - X; 12x112 -(12x1^2)/x211-21 X2^(-2) 499.8 3,7 +0.5X 3/2sqrt(x1) 0.5 -3/sqrt(x1) 10.7 x2 x1 -X2/x1 40 min[3x. 2x Not applicable Not applicable Not applicable 15 XI^(a-1)/x21(1) Not applicable x1 + x3 ax1^(a-1) ax2^(a-1)