Consider the following Cobb-Douglas utility function

u(x_1, x₂)= 2/3 lnx₁ + 1/3lnx₂

(a) (8 points) Find the equation for IC and derive the MRS.

(b) (5 points) Show that MRS is diminishing.

(c) (5 points) Write down the condition for optimal choice and the budget line

for p1 = 1; p2 = 1;m = 3.

(d) (7 points) Find the demand for good 1 and good 2 using part (c).