Question

2. Assume a consumer has as preference relation represented by u(x1, x2) = axi + bx2 with x E C = R4, and a, b > 0. Answer the following: a. Show the preference relation this consumer is convex and strictly monotonic show preferences are not strictly convex for this consumer. b. Graph the indifference curves for this consumer. Now, solve for an explicit expression for the indiffence curve (i.e., x (x1; ū) i constructed in class for an indifference curve with utility level u. c. Compute the MRS between good 1 and good 2, and explain why it coincides with the slope of an indifference curve.

Answer 1

U=ad, tbxz MRS = Museu & Indifferena ше When we draw 2 points in a set og dine a &ioin them the set is convere from the graph there are a 1 3 points [F,G,H) have highes wilty as compared to El 1 At the point Fx, u more as compared to E At point His is more as compared to t. hence at point G H & de are compared at point E hence relation is monotonic. & let us take price be P, el P (for 2 goods) Piae + P2 d =M U = are, tbx - MR So, sh = g {e,= a; & -be n 1 If q> P ;dl, = M; R2 = 0 - H = M ; 0,20 3) If MRS = - 2, 0 to me to hence ate qe an are are consumed of thence cone 3 is tracktomott budget MDUAL CAMERA