Question

Consider a student who purchases education (x) and other goods (y). The student has preferences over these goods given by u(x,y) = ln(x) + 3ln(y). The prices of education and other goods are, respectively, p_x = 10 and p_y = 5, and the student’s income is I = 20.

1. What do limMU_x(x,y) and limMU_y(x,y) tell you about the optimal consumption x→0 y→0 bundle? (2 points)

2. Find an expression for the slope of the indifference curve through the point (x,y). (2 points)

3. Write the Langrangian for the student’s optimization problem and derive the first orderconditions assuming an interior solution.

Answer 1